0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.11 % Command : run_vampire %s %d SAT 0.10/0.31 % Computer : n026.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Wed Jul 30 06:48:19 EDT 2025 0.16/0.31 % CPUTime : 0.16/0.33 This is a TFF_ problem 0.16/0.33 Running first-order model finding 0.16/0.33 Running /export/starexec/sandbox/solver/bin/vampire --mode casc --intent sat -m 16384 --cores 7 -t 120 /export/starexec/sandbox/benchmark/theBenchmark.p 0.17/0.42 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.42 % (5985)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2685282704:gsem=randomized:i=88024:add=on:uhcvi=off:rawr=on_1199 on theBenchmark for (1199ds/88024Mi) 0.17/0.42 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.42 % (5986)dis+10_1_sil=32000:sp=arity:random_seed=1942709439:i=103:fgj=on_1199 on theBenchmark for (1199ds/103Mi) 0.17/0.42 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.42 % (5988)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3216211906:i=131_1199 on theBenchmark for (1199ds/131Mi) 0.17/0.42 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.42 % (5983)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4159719154_1199 on theBenchmark for (1199ds/0Mi) 0.17/0.42 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.42 % (5987)ott+31_1_sil=16000:bce=on:lcm=predicate:newcnf=on:random_seed=1461378420:i=116_1199 on theBenchmark for (1199ds/116Mi) 0.17/0.42 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.42 % (5989)ott-3_16_to=lpo:sil=16000:sp=arity:abs=on:fd=off:rp=on:random_seed=1976727786:i=159:nicw=on:bs=unit_only:fsr=off:amm=off_1199 on theBenchmark for (1199ds/159Mi) 0.17/0.44 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.44 % (5984)dis+11_61:31_drc=ordering:lsd=5:abs=on:bsr=unit_only:rp=on:newcnf=on:random_seed=547548140:i=135531:add=off:rawr=on_1199 on theBenchmark for (1199ds/135531Mi) 0.17/0.48 % (5986)Instruction limit reached! 0.17/0.48 % (5986)------------------------------ 0.17/0.48 % (5986)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 0.17/0.48 % (5986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.17/0.48 % (5986)Termination reason: Instruction limit 0.17/0.48 % (5986)Termination phase: Saturation 0.17/0.48 0.17/0.48 % (5986)Time elapsed: 0.056 s 0.17/0.48 % (5986)Peak memory usage: 9 MB 0.17/0.48 % (5986)Instructions burned: 103 (million) 0.17/0.49 % (5987)Instruction limit reached! 0.17/0.49 % (5987)------------------------------ 0.17/0.49 % (5987)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 0.17/0.49 % (5987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.17/0.49 % (5987)Termination reason: Instruction limit 0.17/0.49 % (5987)Termination phase: Saturation 0.17/0.49 0.17/0.49 % (5987)Time elapsed: 0.060 s 0.17/0.49 % (5987)Peak memory usage: 9 MB 0.17/0.49 % (5987)Instructions burned: 117 (million) 0.17/0.49 % (5988)Instruction limit reached! 0.17/0.49 % (5988)------------------------------ 0.17/0.49 % (5988)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 0.17/0.49 % (5988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.17/0.49 % (5988)Termination reason: Instruction limit 0.17/0.49 % (5988)Termination phase: Saturation 0.17/0.49 0.17/0.49 % (5988)Time elapsed: 0.069 s 0.17/0.49 % (5988)Peak memory usage: 9 MB 0.17/0.49 % (5988)Instructions burned: 131 (million) 0.17/0.51 % (5989)Instruction limit reached! 0.17/0.51 % (5989)------------------------------ 0.17/0.51 % (5989)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 0.17/0.51 % (5989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.17/0.51 % (5989)Termination reason: Instruction limit 0.17/0.51 % (5989)Termination phase: Saturation 0.17/0.51 0.17/0.51 % (5989)Time elapsed: 0.089 s 0.17/0.51 % (5989)Peak memory usage: 9 MB 0.17/0.51 % (5989)Instructions burned: 160 (million) 0.17/0.54 % Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1] 0.17/0.54 % Detected maximum model sizes of [max,max,max,max,max,max,max,max,max,max,2] 0.17/0.54 % TRYING [1,1,1,1,1,1,1,1,1,1,1] 0.17/0.54 % TRYING [1,1,1,1,1,1,1,1,1,1,2] 0.17/0.55 % TRYING [1,1,1,1,1,1,2,1,1,1,2] 0.17/0.55 % TRYING [1,1,1,1,2,1,2,1,1,1,2] 0.17/0.56 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.56 % (5997)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2883372049:i=714:nm=2_1198 on theBenchmark for (1198ds/714Mi) 0.17/0.56 % (5981)Running in auto input_syntax mode. Trying TPTP 0.17/0.56 % (5998)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=966791892:i=131:bd=preordered:fsd=on_1198 on theBenchmark for (1198ds/131Mi) 0.17/0.57 % TRYING [1,1,2,1,2,1,2,1,1,1,2] 1.52/0.57 % (5981)Running in auto input_syntax mode. Trying TPTP 1.52/0.57 % (5999)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1228590843:i=684:slsql=off:nicw=on:bs=unit_only:rawr=on_1198 on theBenchmark for (1198ds/684Mi) 1.52/0.58 % TRYING [2,1,2,1,2,1,2,1,1,1,2] 1.66/0.61 % TRYING [3,1,2,1,2,1,2,1,1,1,2] 1.66/0.62 % TRYING [1] 1.66/0.62 % TRYING [2] 1.95/0.64 % (5998)Instruction limit reached! 1.95/0.64 % (5998)------------------------------ 1.95/0.64 % (5998)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 1.95/0.64 % (5998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.95/0.64 % (5998)Termination reason: Instruction limit 1.95/0.64 % (5998)Termination phase: Saturation 1.95/0.64 1.95/0.64 % (5998)Time elapsed: 0.078 s 1.95/0.64 % (5998)Peak memory usage: 9 MB 1.95/0.64 % (5998)Instructions burned: 132 (million) 2.01/0.65 % TRYING [2,1,2,1,2,1,2,1,1,2,2] 2.01/0.65 % TRYING [3] 2.01/0.67 % TRYING [3,1,2,1,2,1,2,1,1,2,2] 2.33/0.71 % (5981)Running in auto input_syntax mode. Trying TPTP 2.33/0.71 % (6000)ott-21_1_sil=16000:fs=off:random_seed=4027735142:i=180:av=off:fsr=off_1198 on theBenchmark for (1198ds/180Mi) 2.33/0.72 % TRYING [2,1,2,1,2,1,3,1,1,2,2] 2.33/0.73 % (5981)Running in auto input_syntax mode. Trying TPTP 2.33/0.73 % (6004)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3451985898:i=477:bd=all_1196 on theBenchmark for (1196ds/477Mi) 2.58/0.77 % TRYING [2,1,2,1,2,1,2,1,2,2,2] 2.58/0.79 % TRYING [2,1,3,1,2,1,2,1,2,2,2] 2.58/0.82 % TRYING [2,1,3,1,2,1,2,1,3,2,2] 2.58/0.84 % TRYING [4] 3.02/0.86 % Finite Model Found! 3.02/0.86 % SZS status Satisfiable for theBenchmark 3.02/0.86 % (6000)Instruction limit reached! 3.02/0.86 % (6000)------------------------------ 3.02/0.86 % (6000)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 3.02/0.86 % (6000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.02/0.86 % (6000)Termination reason: Instruction limit 3.02/0.86 % (6000)Termination phase: Saturation 3.02/0.86 3.02/0.86 % (6000)Time elapsed: 0.154 s 3.02/0.86 % (6000)Peak memory usage: 8 MB 3.02/0.86 % (6000)Instructions burned: 181 (million) 3.02/0.86 % (5997)Instruction limit reached! 3.02/0.86 % (5997)------------------------------ 3.02/0.86 % (5997)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 3.02/0.86 % (5997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.02/0.86 % (5997)Termination reason: Instruction limit 3.02/0.86 % (5997)Termination phase: Finite model building constraint generation 3.02/0.86 3.02/0.86 % (5997)Time elapsed: 0.303 s 3.02/0.86 % (5997)Peak memory usage: 36 MB 3.02/0.86 % (5997)Instructions burned: 714 (million) 3.02/0.87 % (5983)First to succeed. 3.02/0.87 % (5983)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5981" 3.02/0.87 % (5981)Running in auto input_syntax mode. Trying TPTP 3.02/0.87 % SZS output start FiniteModel for theBenchmark 3.02/0.87 tff('declare_$i1',type,'fmb_$i_1':$i). 3.02/0.87 tff('finite_domain_$i',axiom, 3.02/0.87 ! [X:$i] : ( 3.02/0.87 X = 'fmb_$i_1' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_n_vec_set_set$',type,'A_n_vec_n_vec_set_set$':$tType). 3.02/0.87 tff('declare_A_n_vec_n_vec_set_set$1',type,'fmb_A_n_vec_n_vec_set_set$_1':'A_n_vec_n_vec_set_set$'). 3.02/0.87 tff('declare_A_n_vec_n_vec_set_set$2',type,'fmb_A_n_vec_n_vec_set_set$_2':'A_n_vec_n_vec_set_set$'). 3.02/0.87 tff('declare_A_n_vec_n_vec_set_set$3',type,'fmb_A_n_vec_n_vec_set_set$_3':'A_n_vec_n_vec_set_set$'). 3.02/0.87 tff('finite_domain_A_n_vec_n_vec_set_set$',axiom, 3.02/0.87 ! [X:'A_n_vec_n_vec_set_set$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_n_vec_set_set$_1' | X = 'fmb_A_n_vec_n_vec_set_set$_2' | X = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec_n_vec_set_set$',axiom, 3.02/0.87 'fmb_A_n_vec_n_vec_set_set$_1' != 'fmb_A_n_vec_n_vec_set_set$_2' & 'fmb_A_n_vec_n_vec_set_set$_1' != 'fmb_A_n_vec_n_vec_set_set$_3' & 'fmb_A_n_vec_n_vec_set_set$_2' != 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_set_set$',type,'A_set_set$':$tType). 3.02/0.87 tff('declare_A_set_set$1',type,'fmb_A_set_set$_1':'A_set_set$'). 3.02/0.87 tff('declare_A_set_set$2',type,'fmb_A_set_set$_2':'A_set_set$'). 3.02/0.87 tff('declare_A_set_set$3',type,'fmb_A_set_set$_3':'A_set_set$'). 3.02/0.87 tff('finite_domain_A_set_set$',axiom, 3.02/0.87 ! [X:'A_set_set$'] : ( 3.02/0.87 X = 'fmb_A_set_set$_1' | X = 'fmb_A_set_set$_2' | X = 'fmb_A_set_set$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_set_set$',axiom, 3.02/0.87 'fmb_A_set_set$_1' != 'fmb_A_set_set$_2' & 'fmb_A_set_set$_1' != 'fmb_A_set_set$_3' & 'fmb_A_set_set$_2' != 'fmb_A_set_set$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_set$',type,'A_n_vec_set$':$tType). 3.02/0.87 tff('declare_A_n_vec_set$1',type,'fmb_A_n_vec_set$_1':'A_n_vec_set$'). 3.02/0.87 tff('finite_domain_A_n_vec_set$',axiom, 3.02/0.87 ! [X:'A_n_vec_set$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_set$_1' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_n_vec_bool_fun$',type,'A_n_vec_n_vec_bool_fun$':$tType). 3.02/0.87 tff('declare_A_n_vec_n_vec_bool_fun$1',type,'fmb_A_n_vec_n_vec_bool_fun$_1':'A_n_vec_n_vec_bool_fun$'). 3.02/0.87 tff('declare_A_n_vec_n_vec_bool_fun$2',type,'fmb_A_n_vec_n_vec_bool_fun$_2':'A_n_vec_n_vec_bool_fun$'). 3.02/0.87 tff('declare_A_n_vec_n_vec_bool_fun$3',type,'fmb_A_n_vec_n_vec_bool_fun$_3':'A_n_vec_n_vec_bool_fun$'). 3.02/0.87 tff('finite_domain_A_n_vec_n_vec_bool_fun$',axiom, 3.02/0.87 ! [X:'A_n_vec_n_vec_bool_fun$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_n_vec_bool_fun$_1' | X = 'fmb_A_n_vec_n_vec_bool_fun$_2' | X = 'fmb_A_n_vec_n_vec_bool_fun$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec_n_vec_bool_fun$',axiom, 3.02/0.87 'fmb_A_n_vec_n_vec_bool_fun$_1' != 'fmb_A_n_vec_n_vec_bool_fun$_2' & 'fmb_A_n_vec_n_vec_bool_fun$_1' != 'fmb_A_n_vec_n_vec_bool_fun$_3' & 'fmb_A_n_vec_n_vec_bool_fun$_2' != 'fmb_A_n_vec_n_vec_bool_fun$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_n_vec$',type,'A_n_vec_n_vec$':$tType). 3.02/0.87 tff('declare_A_n_vec_n_vec$1',type,'fmb_A_n_vec_n_vec$_1':'A_n_vec_n_vec$'). 3.02/0.87 tff('declare_A_n_vec_n_vec$2',type,'fmb_A_n_vec_n_vec$_2':'A_n_vec_n_vec$'). 3.02/0.87 tff('finite_domain_A_n_vec_n_vec$',axiom, 3.02/0.87 ! [X:'A_n_vec_n_vec$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_n_vec$_1' | X = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec_n_vec$',axiom, 3.02/0.87 'fmb_A_n_vec_n_vec$_1' != 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_Nat$',type,'Nat$':$tType). 3.02/0.87 tff('declare_Nat$1',type,'fmb_Nat$_1':'Nat$'). 3.02/0.87 tff('declare_Nat$2',type,'fmb_Nat$_2':'Nat$'). 3.02/0.87 tff('declare_Nat$3',type,'fmb_Nat$_3':'Nat$'). 3.02/0.87 tff('finite_domain_Nat$',axiom, 3.02/0.87 ! [X:'Nat$'] : ( 3.02/0.87 X = 'fmb_Nat$_1' | X = 'fmb_Nat$_2' | X = 'fmb_Nat$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_Nat$',axiom, 3.02/0.87 'fmb_Nat$_1' != 'fmb_Nat$_2' & 'fmb_Nat$_1' != 'fmb_Nat$_3' & 'fmb_Nat$_2' != 'fmb_Nat$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_n_vec_set$',type,'A_n_vec_n_vec_set$':$tType). 3.02/0.87 tff('declare_A_n_vec_n_vec_set$1',type,'fmb_A_n_vec_n_vec_set$_1':'A_n_vec_n_vec_set$'). 3.02/0.87 tff('declare_A_n_vec_n_vec_set$2',type,'fmb_A_n_vec_n_vec_set$_2':'A_n_vec_n_vec_set$'). 3.02/0.87 tff('declare_A_n_vec_n_vec_set$3',type,'fmb_A_n_vec_n_vec_set$_3':'A_n_vec_n_vec_set$'). 3.02/0.87 tff('finite_domain_A_n_vec_n_vec_set$',axiom, 3.02/0.87 ! [X:'A_n_vec_n_vec_set$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_n_vec_set$_1' | X = 'fmb_A_n_vec_n_vec_set$_2' | X = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec_n_vec_set$',axiom, 3.02/0.87 'fmb_A_n_vec_n_vec_set$_1' != 'fmb_A_n_vec_n_vec_set$_2' & 'fmb_A_n_vec_n_vec_set$_1' != 'fmb_A_n_vec_n_vec_set$_3' & 'fmb_A_n_vec_n_vec_set$_2' != 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_N$',type,'N$':$tType). 3.02/0.87 tff('declare_N$1',type,'fmb_N$_1':'N$'). 3.02/0.87 tff('finite_domain_N$',axiom, 3.02/0.87 ! [X:'N$'] : ( 3.02/0.87 X = 'fmb_N$_1' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('declare_Num$',type,'Num$':$tType). 3.02/0.87 tff('declare_Num$1',type,'fmb_Num$_1':'Num$'). 3.02/0.87 tff('finite_domain_Num$',axiom, 3.02/0.87 ! [X:'Num$'] : ( 3.02/0.87 X = 'fmb_Num$_1' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('declare_Num_set$',type,'Num_set$':$tType). 3.02/0.87 tff('declare_Num_set$1',type,'fmb_Num_set$_1':'Num_set$'). 3.02/0.87 tff('declare_Num_set$2',type,'fmb_Num_set$_2':'Num_set$'). 3.02/0.87 tff('declare_Num_set$3',type,'fmb_Num_set$_3':'Num_set$'). 3.02/0.87 tff('finite_domain_Num_set$',axiom, 3.02/0.87 ! [X:'Num_set$'] : ( 3.02/0.87 X = 'fmb_Num_set$_1' | X = 'fmb_Num_set$_2' | X = 'fmb_Num_set$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_Num_set$',axiom, 3.02/0.87 'fmb_Num_set$_1' != 'fmb_Num_set$_2' & 'fmb_Num_set$_1' != 'fmb_Num_set$_3' & 'fmb_Num_set$_2' != 'fmb_Num_set$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff(declare_tlbool,type,tlbool:$tType). 3.02/0.87 tff(declare_tlbool1,type,fmb_tlbool_1:tlbool). 3.02/0.87 tff(declare_tlbool2,type,fmb_tlbool_2:tlbool). 3.02/0.87 tff(finite_domain_tlbool,axiom, 3.02/0.87 ! [X:tlbool] : ( 3.02/0.87 X = fmb_tlbool_1 | X = fmb_tlbool_2 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff(distinct_domain_tlbool,axiom, 3.02/0.87 fmb_tlbool_1 != fmb_tlbool_2 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_bool_fun$',type,'A_bool_fun$':$tType). 3.02/0.87 tff('declare_A_bool_fun$1',type,'fmb_A_bool_fun$_1':'A_bool_fun$'). 3.02/0.87 tff('declare_A_bool_fun$2',type,'fmb_A_bool_fun$_2':'A_bool_fun$'). 3.02/0.87 tff('declare_A_bool_fun$3',type,'fmb_A_bool_fun$_3':'A_bool_fun$'). 3.02/0.87 tff('finite_domain_A_bool_fun$',axiom, 3.02/0.87 ! [X:'A_bool_fun$'] : ( 3.02/0.87 X = 'fmb_A_bool_fun$_1' | X = 'fmb_A_bool_fun$_2' | X = 'fmb_A_bool_fun$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_bool_fun$',axiom, 3.02/0.87 'fmb_A_bool_fun$_1' != 'fmb_A_bool_fun$_2' & 'fmb_A_bool_fun$_1' != 'fmb_A_bool_fun$_3' & 'fmb_A_bool_fun$_2' != 'fmb_A_bool_fun$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_set$',type,'A_set$':$tType). 3.02/0.87 tff('declare_A_set$1',type,'fmb_A_set$_1':'A_set$'). 3.02/0.87 tff('finite_domain_A_set$',axiom, 3.02/0.87 ! [X:'A_set$'] : ( 3.02/0.87 X = 'fmb_A_set$_1' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_set_set$',type,'A_n_vec_set_set$':$tType). 3.02/0.87 tff('declare_A_n_vec_set_set$1',type,'fmb_A_n_vec_set_set$_1':'A_n_vec_set_set$'). 3.02/0.87 tff('declare_A_n_vec_set_set$2',type,'fmb_A_n_vec_set_set$_2':'A_n_vec_set_set$'). 3.02/0.87 tff('declare_A_n_vec_set_set$3',type,'fmb_A_n_vec_set_set$_3':'A_n_vec_set_set$'). 3.02/0.87 tff('finite_domain_A_n_vec_set_set$',axiom, 3.02/0.87 ! [X:'A_n_vec_set_set$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_set_set$_1' | X = 'fmb_A_n_vec_set_set$_2' | X = 'fmb_A_n_vec_set_set$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec_set_set$',axiom, 3.02/0.87 'fmb_A_n_vec_set_set$_1' != 'fmb_A_n_vec_set_set$_2' & 'fmb_A_n_vec_set_set$_1' != 'fmb_A_n_vec_set_set$_3' & 'fmb_A_n_vec_set_set$_2' != 'fmb_A_n_vec_set_set$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A$',type,'A$':$tType). 3.02/0.87 tff('declare_A$1',type,'fmb_A$_1':'A$'). 3.02/0.87 tff('declare_A$2',type,'fmb_A$_2':'A$'). 3.02/0.87 tff('finite_domain_A$',axiom, 3.02/0.87 ! [X:'A$'] : ( 3.02/0.87 X = 'fmb_A$_1' | X = 'fmb_A$_2' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A$',axiom, 3.02/0.87 'fmb_A$_1' != 'fmb_A$_2' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec$',type,'A_n_vec$':$tType). 3.02/0.87 tff('declare_A_n_vec$1',type,'fmb_A_n_vec$_1':'A_n_vec$'). 3.02/0.87 tff('declare_A_n_vec$2',type,'fmb_A_n_vec$_2':'A_n_vec$'). 3.02/0.87 tff('finite_domain_A_n_vec$',axiom, 3.02/0.87 ! [X:'A_n_vec$'] : ( 3.02/0.87 X = 'fmb_A_n_vec$_1' | X = 'fmb_A_n_vec$_2' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec$',axiom, 3.02/0.87 'fmb_A_n_vec$_1' != 'fmb_A_n_vec$_2' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_a_fun$',type,'A_a_fun$':$tType). 3.02/0.87 tff('declare_A_a_fun$1',type,'fmb_A_a_fun$_1':'A_a_fun$'). 3.02/0.87 tff('declare_A_a_fun$2',type,'fmb_A_a_fun$_2':'A_a_fun$'). 3.02/0.87 tff('declare_A_a_fun$3',type,'fmb_A_a_fun$_3':'A_a_fun$'). 3.02/0.87 tff('finite_domain_A_a_fun$',axiom, 3.02/0.87 ! [X:'A_a_fun$'] : ( 3.02/0.87 X = 'fmb_A_a_fun$_1' | X = 'fmb_A_a_fun$_2' | X = 'fmb_A_a_fun$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_a_fun$',axiom, 3.02/0.87 'fmb_A_a_fun$_1' != 'fmb_A_a_fun$_2' & 'fmb_A_a_fun$_1' != 'fmb_A_a_fun$_3' & 'fmb_A_a_fun$_2' != 'fmb_A_a_fun$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_n_vec_n_vec$',type,'A_n_vec_n_vec_n_vec$':$tType). 3.02/0.87 tff('declare_A_n_vec_n_vec_n_vec$1',type,'fmb_A_n_vec_n_vec_n_vec$_1':'A_n_vec_n_vec_n_vec$'). 3.02/0.87 tff('declare_A_n_vec_n_vec_n_vec$2',type,'fmb_A_n_vec_n_vec_n_vec$_2':'A_n_vec_n_vec_n_vec$'). 3.02/0.87 tff('finite_domain_A_n_vec_n_vec_n_vec$',axiom, 3.02/0.87 ! [X:'A_n_vec_n_vec_n_vec$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_n_vec_n_vec$_1' | X = 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec_n_vec_n_vec$',axiom, 3.02/0.87 'fmb_A_n_vec_n_vec_n_vec$_1' != 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_A_n_vec_bool_fun$',type,'A_n_vec_bool_fun$':$tType). 3.02/0.87 tff('declare_A_n_vec_bool_fun$1',type,'fmb_A_n_vec_bool_fun$_1':'A_n_vec_bool_fun$'). 3.02/0.87 tff('declare_A_n_vec_bool_fun$2',type,'fmb_A_n_vec_bool_fun$_2':'A_n_vec_bool_fun$'). 3.02/0.87 tff('declare_A_n_vec_bool_fun$3',type,'fmb_A_n_vec_bool_fun$_3':'A_n_vec_bool_fun$'). 3.02/0.87 tff('finite_domain_A_n_vec_bool_fun$',axiom, 3.02/0.87 ! [X:'A_n_vec_bool_fun$'] : ( 3.02/0.87 X = 'fmb_A_n_vec_bool_fun$_1' | X = 'fmb_A_n_vec_bool_fun$_2' | X = 'fmb_A_n_vec_bool_fun$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_A_n_vec_bool_fun$',axiom, 3.02/0.87 'fmb_A_n_vec_bool_fun$_1' != 'fmb_A_n_vec_bool_fun$_2' & 'fmb_A_n_vec_bool_fun$_1' != 'fmb_A_n_vec_bool_fun$_3' & 'fmb_A_n_vec_bool_fun$_2' != 'fmb_A_n_vec_bool_fun$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_N_a_n_vec_n_vec_fun$',type,'N_a_n_vec_n_vec_fun$':$tType). 3.02/0.87 tff('declare_N_a_n_vec_n_vec_fun$1',type,'fmb_N_a_n_vec_n_vec_fun$_1':'N_a_n_vec_n_vec_fun$'). 3.02/0.87 tff('declare_N_a_n_vec_n_vec_fun$2',type,'fmb_N_a_n_vec_n_vec_fun$_2':'N_a_n_vec_n_vec_fun$'). 3.02/0.87 tff('declare_N_a_n_vec_n_vec_fun$3',type,'fmb_N_a_n_vec_n_vec_fun$_3':'N_a_n_vec_n_vec_fun$'). 3.02/0.87 tff('finite_domain_N_a_n_vec_n_vec_fun$',axiom, 3.02/0.87 ! [X:'N_a_n_vec_n_vec_fun$'] : ( 3.02/0.87 X = 'fmb_N_a_n_vec_n_vec_fun$_1' | X = 'fmb_N_a_n_vec_n_vec_fun$_2' | X = 'fmb_N_a_n_vec_n_vec_fun$_3' 3.02/0.87 ) ). 3.02/0.87 3.02/0.87 tff('distinct_domain_N_a_n_vec_n_vec_fun$',axiom, 3.02/0.87 'fmb_N_a_n_vec_n_vec_fun$_1' != 'fmb_N_a_n_vec_n_vec_fun$_2' & 'fmb_N_a_n_vec_n_vec_fun$_1' != 'fmb_N_a_n_vec_n_vec_fun$_3' & 'fmb_N_a_n_vec_n_vec_fun$_2' != 'fmb_N_a_n_vec_n_vec_fun$_3' 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_invertible$',type,'invertible$':'A_n_vec_n_vec_bool_fun$'). 3.02/0.87 tff('invertible$_definition',axiom,'invertible$' = 'fmb_A_n_vec_n_vec_bool_fun$_1'). 3.02/0.87 tff('declare_zero$d',type,'zero$d':'A_set$'). 3.02/0.87 tff('zero$d_definition',axiom,'zero$d' = 'fmb_A_set$_1'). 3.02/0.87 tff('declare_zero$c',type,'zero$c':'A_n_vec$'). 3.02/0.87 tff('zero$c_definition',axiom,'zero$c' = 'fmb_A_n_vec$_1'). 3.02/0.87 tff('declare_zero$f',type,'zero$f':'A_n_vec_set$'). 3.02/0.87 tff('zero$f_definition',axiom,'zero$f' = 'fmb_A_n_vec_set$_1'). 3.02/0.87 tff('declare_one$',type,'one$':'A$'). 3.02/0.87 tff('one$_definition',axiom,'one$' = 'fmb_A$_1'). 3.02/0.87 tff('declare_zero$b',type,'zero$b':'A_n_vec_n_vec_n_vec$'). 3.02/0.87 tff('zero$b_definition',axiom,'zero$b' = 'fmb_A_n_vec_n_vec_n_vec$_1'). 3.02/0.87 tff(declare_tltrue,type,tltrue:tlbool). 3.02/0.87 tff(tltrue_definition,axiom,tltrue = fmb_tlbool_1). 3.02/0.87 tff('declare_one$b',type,'one$b':'A_n_vec_n_vec$'). 3.02/0.87 tff('one$b_definition',axiom,'one$b' = 'fmb_A_n_vec_n_vec$_1'). 3.02/0.87 tff('declare_a$',type,'a$':'A_n_vec_n_vec$'). 3.02/0.87 tff('a$_definition',axiom,'a$' = 'fmb_A_n_vec_n_vec$_1'). 3.02/0.87 tff('declare_reduced_row_echelon_form$',type,'reduced_row_echelon_form$':'A_n_vec_n_vec_bool_fun$'). 3.02/0.87 tff('reduced_row_echelon_form$_definition',axiom,'reduced_row_echelon_form$' = 'fmb_A_n_vec_n_vec_bool_fun$_2'). 3.02/0.87 tff('declare_one$a',type,'one$a':'A_n_vec$'). 3.02/0.87 tff('one$a_definition',axiom,'one$a' = 'fmb_A_n_vec$_2'). 3.02/0.87 tff('declare_zero$a',type,'zero$a':'A_n_vec_n_vec$'). 3.02/0.87 tff('zero$a_definition',axiom,'zero$a' = 'fmb_A_n_vec_n_vec$_2'). 3.02/0.87 tff('declare_orthogonal_matrix$',type,'orthogonal_matrix$':'A_n_vec_n_vec_bool_fun$'). 3.02/0.87 tff('orthogonal_matrix$_definition',axiom,'orthogonal_matrix$' = 'fmb_A_n_vec_n_vec_bool_fun$_1'). 3.02/0.87 tff('declare_one$c',type,'one$c':'A_set$'). 3.02/0.87 tff('one$c_definition',axiom,'one$c' = 'fmb_A_set$_1'). 3.02/0.87 tff('declare_zero$',type,'zero$':'A$'). 3.02/0.87 tff('zero$_definition',axiom,'zero$' = 'fmb_A$_2'). 3.02/0.87 tff(declare_tlfalse,type,tlfalse:tlbool). 3.02/0.87 tff(tlfalse_definition,axiom,tlfalse = fmb_tlbool_2). 3.02/0.87 tff('declare_zero$e',type,'zero$e':'A_n_vec_n_vec_set$'). 3.02/0.87 tff('zero$e_definition',axiom,'zero$e' = 'fmb_A_n_vec_n_vec_set$_1'). 3.02/0.87 tff('declare_p$',type,'p$':'A_n_vec_n_vec$'). 3.02/0.87 tff('p$_definition',axiom,'p$' = 'fmb_A_n_vec_n_vec$_1'). 3.02/0.87 tff('declare_numeral$a',type,'numeral$a': ('Num$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_numeral$a',axiom, 3.02/0.87 'numeral$a'('fmb_Num$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_uu$',type,'uu$': ('A_set$') > 'A_bool_fun$'). 3.02/0.87 tff('function_uu$',axiom, 3.02/0.87 'uu$'('fmb_A_set$_1') = 'fmb_A_bool_fun$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_dbl_inc$a',type,'dbl_inc$a': ('A_n_vec$') > 'A_n_vec$'). 3.02/0.87 tff('function_dbl_inc$a',axiom, 3.02/0.87 'dbl_inc$a'('fmb_A_n_vec$_1') = 'fmb_A_n_vec$_2' 3.02/0.87 & 'dbl_inc$a'('fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_mat$',type,'mat$': ('A$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_mat$',axiom, 3.02/0.87 'mat$'('fmb_A$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'mat$'('fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_dbl_inc$',type,'dbl_inc$': ('A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_dbl_inc$',axiom, 3.02/0.87 'dbl_inc$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'dbl_inc$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_uub$',type,'uub$': ('A_n_vec_set$') > 'A_n_vec_bool_fun$'). 3.02/0.87 tff('function_uub$',axiom, 3.02/0.87 'uub$'('fmb_A_n_vec_set$_1') = 'fmb_A_n_vec_bool_fun$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_matrix_vector_mult$',type,'matrix_vector_mult$': ('A_n_vec_n_vec$' * 'A_n_vec$') > 'A_n_vec$'). 3.02/0.87 tff('function_matrix_vector_mult$',axiom, 3.02/0.87 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' 3.02/0.87 & 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' 3.02/0.87 & 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' 3.02/0.87 & 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_times$d',type,'times$d': ('A_n_vec_set$' * 'A_n_vec_set$') > 'A_n_vec_set$'). 3.02/0.87 tff('function_times$d',axiom, 3.02/0.87 'times$d'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set$_1') = 'fmb_A_n_vec_set$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_vector_matrix_mult$a',type,'vector_matrix_mult$a': ('A_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec$'). 3.02/0.87 tff('function_vector_matrix_mult$a',axiom, 3.02/0.87 'vector_matrix_mult$a'('fmb_A_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec$_1' 3.02/0.87 & 'vector_matrix_mult$a'('fmb_A_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec$_1' 3.02/0.87 & 'vector_matrix_mult$a'('fmb_A_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec$_2' 3.02/0.87 & 'vector_matrix_mult$a'('fmb_A_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_axis$',type,'axis$': ('N$' * 'A_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_axis$',axiom, 3.02/0.87 'axis$'('fmb_N$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'axis$'('fmb_N$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_columnvector$',type,'columnvector$': ('A_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_columnvector$',axiom, 3.02/0.87 'columnvector$'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'columnvector$'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_gauss_Jordan$',type,'gauss_Jordan$': ('A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_gauss_Jordan$',axiom, 3.02/0.87 'gauss_Jordan$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'gauss_Jordan$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_plus$g',type,'plus$g': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_plus$g',axiom, 3.02/0.87 'plus$g'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'plus$g'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'plus$g'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'plus$g'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_times$g',type,'times$g': ('Num$' * 'Num$') > 'Num$'). 3.02/0.87 tff('function_times$g',axiom, 3.02/0.87 'times$g'('fmb_Num$_1','fmb_Num$_1') = 'fmb_Num$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_collect$a',type,'collect$a': ('A_n_vec_n_vec_bool_fun$') > 'A_n_vec_n_vec_set$'). 3.02/0.87 tff('function_collect$a',axiom, 3.02/0.87 'collect$a'('fmb_A_n_vec_n_vec_bool_fun$_1') = 'fmb_A_n_vec_n_vec_set$_2' 3.02/0.87 & 'collect$a'('fmb_A_n_vec_n_vec_bool_fun$_2') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.87 & 'collect$a'('fmb_A_n_vec_n_vec_bool_fun$_3') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_axis$a',type,'axis$a': ('N$' * 'A$') > 'A_n_vec$'). 3.02/0.87 tff('function_axis$a',axiom, 3.02/0.87 'axis$a'('fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec$_2' 3.02/0.87 & 'axis$a'('fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_plus$c',type,'plus$c': ('A_n_vec_n_vec_set_set$' * 'A_n_vec_n_vec_set_set$') > 'A_n_vec_n_vec_set_set$'). 3.02/0.87 tff('function_plus$c',axiom, 3.02/0.87 'plus$c'('fmb_A_n_vec_n_vec_set_set$_1','fmb_A_n_vec_n_vec_set_set$_1') = 'fmb_A_n_vec_n_vec_set_set$_2' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_1','fmb_A_n_vec_n_vec_set_set$_2') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_1','fmb_A_n_vec_n_vec_set_set$_3') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_2','fmb_A_n_vec_n_vec_set_set$_1') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_2','fmb_A_n_vec_n_vec_set_set$_2') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_2','fmb_A_n_vec_n_vec_set_set$_3') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_3','fmb_A_n_vec_n_vec_set_set$_1') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_3','fmb_A_n_vec_n_vec_set_set$_2') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 & 'plus$c'('fmb_A_n_vec_n_vec_set_set$_3','fmb_A_n_vec_n_vec_set_set$_3') = 'fmb_A_n_vec_n_vec_set_set$_3' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_plus$i',type,'plus$i': ('A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$') > 'A_n_vec_n_vec_n_vec$'). 3.02/0.87 tff('function_plus$i',axiom, 3.02/0.87 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' 3.02/0.87 & 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.87 & 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.87 & 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_vec$a',type,'vec$a': ('A_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_vec$a',axiom, 3.02/0.87 'vec$a'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'vec$a'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_times$a',type,'times$a': ('A_n_vec$' * 'A_n_vec$') > 'A_n_vec$'). 3.02/0.87 tff('function_times$a',axiom, 3.02/0.87 'times$a'('fmb_A_n_vec$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' 3.02/0.87 & 'times$a'('fmb_A_n_vec$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_1' 3.02/0.87 & 'times$a'('fmb_A_n_vec$_2','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' 3.02/0.87 & 'times$a'('fmb_A_n_vec$_2','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_times$',type,'times$': ('A$' * 'A$') > 'A$'). 3.02/0.87 tff('function_times$',axiom, 3.02/0.87 'times$'('fmb_A$_1','fmb_A$_1') = 'fmb_A$_1' 3.02/0.87 & 'times$'('fmb_A$_1','fmb_A$_2') = 'fmb_A$_2' 3.02/0.87 & 'times$'('fmb_A$_2','fmb_A$_1') = 'fmb_A$_2' 3.02/0.87 & 'times$'('fmb_A$_2','fmb_A$_2') = 'fmb_A$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_collect$',type,'collect$': ('A_bool_fun$') > 'A_set$'). 3.02/0.87 tff('function_collect$',axiom, 3.02/0.87 'collect$'('fmb_A_bool_fun$_1') = 'fmb_A_set$_1' 3.02/0.87 & 'collect$'('fmb_A_bool_fun$_2') = 'fmb_A_set$_1' 3.02/0.87 & 'collect$'('fmb_A_bool_fun$_3') = 'fmb_A_set$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_matrix_inv$',type,'matrix_inv$': ('A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_matrix_inv$',axiom, 3.02/0.87 'matrix_inv$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'matrix_inv$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_equivalent_matrices$',type,'equivalent_matrices$': ('A_n_vec_n_vec$') > 'A_n_vec_n_vec_bool_fun$'). 3.02/0.87 tff('function_equivalent_matrices$',axiom, 3.02/0.87 'equivalent_matrices$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_bool_fun$_1' 3.02/0.87 & 'equivalent_matrices$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_bool_fun$_3' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_plus$a',type,'plus$a': ('A_set_set$' * 'A_set_set$') > 'A_set_set$'). 3.02/0.87 tff('function_plus$a',axiom, 3.02/0.87 'plus$a'('fmb_A_set_set$_1','fmb_A_set_set$_1') = 'fmb_A_set_set$_2' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_1','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_1','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_2','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_2','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_2','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_3','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_3','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' 3.02/0.87 & 'plus$a'('fmb_A_set_set$_3','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_plus$',type,'plus$': ('A_set$' * 'A_set$') > 'A_set$'). 3.02/0.87 tff('function_plus$',axiom, 3.02/0.87 'plus$'('fmb_A_set$_1','fmb_A_set$_1') = 'fmb_A_set$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_plus$h',type,'plus$h': ('A$' * 'A$') > 'A$'). 3.02/0.87 tff('function_plus$h',axiom, 3.02/0.87 'plus$h'('fmb_A$_1','fmb_A$_1') = 'fmb_A$_2' 3.02/0.87 & 'plus$h'('fmb_A$_1','fmb_A$_2') = 'fmb_A$_1' 3.02/0.87 & 'plus$h'('fmb_A$_2','fmb_A$_1') = 'fmb_A$_1' 3.02/0.87 & 'plus$h'('fmb_A$_2','fmb_A$_2') = 'fmb_A$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_row_add$',type,'row_add$': ('A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_row_add$',axiom, 3.02/0.87 'row_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'row_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'row_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'row_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_numeral$',type,'numeral$': ('Num$') > 'A_n_vec$'). 3.02/0.87 tff('function_numeral$',axiom, 3.02/0.87 'numeral$'('fmb_Num$_1') = 'fmb_A_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_rowvector$',type,'rowvector$': ('A_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_rowvector$',axiom, 3.02/0.87 'rowvector$'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'rowvector$'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_gauss_Jordan_upt_k$',type,'gauss_Jordan_upt_k$': ('A_n_vec_n_vec$' * 'Nat$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_gauss_Jordan_upt_k$',axiom, 3.02/0.87 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_1','fmb_Nat$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_1','fmb_Nat$_2') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_1','fmb_Nat$_3') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_2','fmb_Nat$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_2','fmb_Nat$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_2','fmb_Nat$_3') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_mat$a',type,'mat$a': ('A_n_vec$') > 'A_n_vec_n_vec_n_vec$'). 3.02/0.87 tff('function_mat$a',axiom, 3.02/0.87 'mat$a'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.87 & 'mat$a'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_collect$b',type,'collect$b': ('A_n_vec_bool_fun$') > 'A_n_vec_set$'). 3.02/0.87 tff('function_collect$b',axiom, 3.02/0.87 'collect$b'('fmb_A_n_vec_bool_fun$_1') = 'fmb_A_n_vec_set$_1' 3.02/0.87 & 'collect$b'('fmb_A_n_vec_bool_fun$_2') = 'fmb_A_n_vec_set$_1' 3.02/0.87 & 'collect$b'('fmb_A_n_vec_bool_fun$_3') = 'fmb_A_n_vec_set$_1' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_mult_column$',type,'mult_column$': ('A_n_vec_n_vec$' * 'N$' * 'A$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_mult_column$',axiom, 3.02/0.87 'mult_column$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.87 & 'mult_column$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'mult_column$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'mult_column$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 3.02/0.87 ). 3.02/0.87 3.02/0.87 tff('declare_column_add$',type,'column_add$': ('A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$') > 'A_n_vec_n_vec$'). 3.02/0.87 tff('function_column_add$',axiom, 3.02/0.87 'column_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'column_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'column_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.87 & 'column_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_plus$b',type,'plus$b': ('A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$') > 'A_n_vec_n_vec_set$'). 3.02/0.88 tff('function_plus$b',axiom, 3.02/0.88 'plus$b'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_2' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_2' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 & 'plus$b'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_divide$',type,'divide$': ('A$') > 'A_a_fun$'). 3.02/0.88 tff('function_divide$',axiom, 3.02/0.88 'divide$'('fmb_A$_1') = 'fmb_A_a_fun$_2' 3.02/0.88 & 'divide$'('fmb_A$_2') = 'fmb_A_a_fun$_1' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_matrix_matrix_mult$',type,'matrix_matrix_mult$': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_matrix_matrix_mult$',axiom, 3.02/0.88 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_transpose$',type,'transpose$': ('A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_transpose$',axiom, 3.02/0.88 'transpose$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'transpose$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_fun_app$d',type,'fun_app$d': ('A_a_fun$' * 'A$') > 'A$'). 3.02/0.88 tff('function_fun_app$d',axiom, 3.02/0.88 'fun_app$d'('fmb_A_a_fun$_1','fmb_A$_1') = 'fmb_A$_2' 3.02/0.88 & 'fun_app$d'('fmb_A_a_fun$_1','fmb_A$_2') = 'fmb_A$_2' 3.02/0.88 & 'fun_app$d'('fmb_A_a_fun$_2','fmb_A$_1') = 'fmb_A$_1' 3.02/0.88 & 'fun_app$d'('fmb_A_a_fun$_2','fmb_A$_2') = 'fmb_A$_2' 3.02/0.88 & 'fun_app$d'('fmb_A_a_fun$_3','fmb_A$_1') = 'fmb_A$_2' 3.02/0.88 & 'fun_app$d'('fmb_A_a_fun$_3','fmb_A$_2') = 'fmb_A$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_uua$',type,'uua$': ('A_n_vec_n_vec_set$') > 'A_n_vec_n_vec_bool_fun$'). 3.02/0.88 tff('function_uua$',axiom, 3.02/0.88 'uua$'('fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_bool_fun$_3' 3.02/0.88 & 'uua$'('fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_bool_fun$_1' 3.02/0.88 & 'uua$'('fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_bool_fun$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_matrix_vector_mult$a',type,'matrix_vector_mult$a': ('A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_matrix_vector_mult$a',axiom, 3.02/0.88 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_column$',type,'column$': ('N$' * 'A_n_vec_n_vec$') > 'A_n_vec$'). 3.02/0.88 tff('function_column$',axiom, 3.02/0.88 'column$'('fmb_N$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec$_2' 3.02/0.88 & 'column$'('fmb_N$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec$_1' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_vec$',type,'vec$': ('A$') > 'A_n_vec$'). 3.02/0.88 tff('function_vec$',axiom, 3.02/0.88 'vec$'('fmb_A$_1') = 'fmb_A_n_vec$_2' 3.02/0.88 & 'vec$'('fmb_A$_2') = 'fmb_A_n_vec$_1' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_times$b',type,'times$b': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_times$b',axiom, 3.02/0.88 'times$b'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'times$b'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'times$b'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'times$b'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_plus$d',type,'plus$d': ('A_n_vec$' * 'A_n_vec$') > 'A_n_vec$'). 3.02/0.88 tff('function_plus$d',axiom, 3.02/0.88 'plus$d'('fmb_A_n_vec$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' 3.02/0.88 & 'plus$d'('fmb_A_n_vec$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' 3.02/0.88 & 'plus$d'('fmb_A_n_vec$_2','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_2' 3.02/0.88 & 'plus$d'('fmb_A_n_vec$_2','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_1' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_fun_app$c',type,'fun_app$c': ('N_a_n_vec_n_vec_fun$' * 'N$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_fun_app$c',axiom, 3.02/0.88 'fun_app$c'('fmb_N_a_n_vec_n_vec_fun$_1','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'fun_app$c'('fmb_N_a_n_vec_n_vec_fun$_2','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'fun_app$c'('fmb_N_a_n_vec_n_vec_fun$_3','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_numeral$b',type,'numeral$b': ('Num$') > 'A$'). 3.02/0.88 tff('function_numeral$b',axiom, 3.02/0.88 'numeral$b'('fmb_Num$_1') = 'fmb_A$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_plus$e',type,'plus$e': ('A_n_vec_set$' * 'A_n_vec_set$') > 'A_n_vec_set$'). 3.02/0.88 tff('function_plus$e',axiom, 3.02/0.88 'plus$e'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set$_1') = 'fmb_A_n_vec_set$_1' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_times$h',type,'times$h': ('Num_set$' * 'Num_set$') > 'Num_set$'). 3.02/0.88 tff('function_times$h',axiom, 3.02/0.88 'times$h'('fmb_Num_set$_1','fmb_Num_set$_1') = 'fmb_Num_set$_2' 3.02/0.88 & 'times$h'('fmb_Num_set$_1','fmb_Num_set$_2') = 'fmb_Num_set$_3' 3.02/0.88 & 'times$h'('fmb_Num_set$_1','fmb_Num_set$_3') = 'fmb_Num_set$_3' 3.02/0.88 & 'times$h'('fmb_Num_set$_2','fmb_Num_set$_1') = 'fmb_Num_set$_3' 3.02/0.88 & 'times$h'('fmb_Num_set$_2','fmb_Num_set$_2') = 'fmb_Num_set$_3' 3.02/0.88 & 'times$h'('fmb_Num_set$_2','fmb_Num_set$_3') = 'fmb_Num_set$_3' 3.02/0.88 & 'times$h'('fmb_Num_set$_3','fmb_Num_set$_1') = 'fmb_Num_set$_3' 3.02/0.88 & 'times$h'('fmb_Num_set$_3','fmb_Num_set$_2') = 'fmb_Num_set$_3' 3.02/0.88 & 'times$h'('fmb_Num_set$_3','fmb_Num_set$_3') = 'fmb_Num_set$_3' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_similar_matrices$',type,'similar_matrices$': ('A_n_vec_n_vec$') > 'A_n_vec_n_vec_bool_fun$'). 3.02/0.88 tff('function_similar_matrices$',axiom, 3.02/0.88 'similar_matrices$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_bool_fun$_1' 3.02/0.88 & 'similar_matrices$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_bool_fun$_3' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_transpose$a',type,'transpose$a': ('A_n_vec_n_vec_n_vec$') > 'A_n_vec_n_vec_n_vec$'). 3.02/0.88 tff('function_transpose$a',axiom, 3.02/0.88 'transpose$a'('fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' 3.02/0.88 & 'transpose$a'('fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_times$c',type,'times$c': ('A_set$' * 'A_set$') > 'A_set$'). 3.02/0.88 tff('function_times$c',axiom, 3.02/0.88 'times$c'('fmb_A_set$_1','fmb_A_set$_1') = 'fmb_A_set$_1' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_interchange_columns$',type,'interchange_columns$': ('A_n_vec_n_vec$' * 'N$' * 'N$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_interchange_columns$',axiom, 3.02/0.88 'interchange_columns$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'interchange_columns$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_vector_matrix_mult$',type,'vector_matrix_mult$': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_vector_matrix_mult$',axiom, 3.02/0.88 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_mult_row$',type,'mult_row$': ('A_n_vec_n_vec$' * 'N$' * 'A$') > 'A_n_vec_n_vec$'). 3.02/0.88 tff('function_mult_row$',axiom, 3.02/0.88 'mult_row$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_1' 3.02/0.88 & 'mult_row$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'mult_row$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 & 'mult_row$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_matrix_matrix_mult$a',type,'matrix_matrix_mult$a': ('A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$') > 'A_n_vec_n_vec_n_vec$'). 3.02/0.88 tff('function_matrix_matrix_mult$a',axiom, 3.02/0.88 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' 3.02/0.88 & 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_1' 3.02/0.88 & 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' 3.02/0.88 & 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_dbl_inc$b',type,'dbl_inc$b': ('A$') > 'A$'). 3.02/0.88 tff('function_dbl_inc$b',axiom, 3.02/0.88 'dbl_inc$b'('fmb_A$_1') = 'fmb_A$_1' 3.02/0.88 & 'dbl_inc$b'('fmb_A$_2') = 'fmb_A$_1' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_interchange_rows$',type,'interchange_rows$': ('A_n_vec_n_vec$' * 'N$') > 'N_a_n_vec_n_vec_fun$'). 3.02/0.88 tff('function_interchange_rows$',axiom, 3.02/0.88 'interchange_rows$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1') = 'fmb_N_a_n_vec_n_vec_fun$_2' 3.02/0.88 & 'interchange_rows$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1') = 'fmb_N_a_n_vec_n_vec_fun$_3' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_times$e',type,'times$e': ('A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$') > 'A_n_vec_n_vec_set$'). 3.02/0.88 tff('function_times$e',axiom, 3.02/0.88 'times$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_2' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 & 'times$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_times$f',type,'times$f': ('A_set_set$' * 'A_set_set$') > 'A_set_set$'). 3.02/0.88 tff('function_times$f',axiom, 3.02/0.88 'times$f'('fmb_A_set_set$_1','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_1','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_1','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_2','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_2','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_2','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_3','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_3','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' 3.02/0.88 & 'times$f'('fmb_A_set_set$_3','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_plus$f',type,'plus$f': ('A_n_vec_set_set$' * 'A_n_vec_set_set$') > 'A_n_vec_set_set$'). 3.02/0.88 tff('function_plus$f',axiom, 3.02/0.88 'plus$f'('fmb_A_n_vec_set_set$_1','fmb_A_n_vec_set_set$_1') = 'fmb_A_n_vec_set_set$_2' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_1','fmb_A_n_vec_set_set$_2') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_1','fmb_A_n_vec_set_set$_3') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_2','fmb_A_n_vec_set_set$_1') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_2','fmb_A_n_vec_set_set$_2') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_2','fmb_A_n_vec_set_set$_3') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_3','fmb_A_n_vec_set_set$_1') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_3','fmb_A_n_vec_set_set$_2') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 & 'plus$f'('fmb_A_n_vec_set_set$_3','fmb_A_n_vec_set_set$_3') = 'fmb_A_n_vec_set_set$_3' 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_member$f',type,'member$f': ('A_n_vec_set$' * 'A_n_vec_set_set$') > $o). 3.02/0.88 tff('predicate_member$f',axiom, 3.02/0.88 ~'member$f'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set_set$_1') 3.02/0.88 & ~'member$f'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set_set$_2') 3.02/0.88 & ~'member$f'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set_set$_3') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_member$',type,'member$': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$') > $o). 3.02/0.88 tff('predicate_member$',axiom, 3.02/0.88 ~'member$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_set$_1') 3.02/0.88 & 'member$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_set$_2') 3.02/0.88 & 'member$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_set$_3') 3.02/0.88 & 'member$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_set$_1') 3.02/0.88 & ~'member$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_set$_2') 3.02/0.88 & 'member$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_set$_3') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_member$e',type,'member$e': ('A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set_set$') > $o). 3.02/0.88 tff('predicate_member$e',axiom, 3.02/0.88 ~'member$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set_set$_1') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set_set$_2') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set_set$_3') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set_set$_1') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set_set$_2') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set_set$_3') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set_set$_1') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set_set$_2') 3.02/0.88 & ~'member$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set_set$_3') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_member$d',type,'member$d': ('Num$' * 'Num_set$') > $o). 3.02/0.88 tff('predicate_member$d',axiom, 3.02/0.88 'member$d'('fmb_Num$_1','fmb_Num_set$_1') 3.02/0.88 & 'member$d'('fmb_Num$_1','fmb_Num_set$_2') 3.02/0.88 & 'member$d'('fmb_Num$_1','fmb_Num_set$_3') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_member$b',type,'member$b': ('A$' * 'A_set$') > $o). 3.02/0.88 tff('predicate_member$b',axiom, 3.02/0.88 ~'member$b'('fmb_A$_1','fmb_A_set$_1') 3.02/0.88 & ~'member$b'('fmb_A$_2','fmb_A_set$_1') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_fun_app$b',type,'fun_app$b': ('A_bool_fun$' * 'A$') > $o). 3.02/0.88 tff('predicate_fun_app$b',axiom, 3.02/0.88 ~'fun_app$b'('fmb_A_bool_fun$_1','fmb_A$_1') 3.02/0.88 & ~'fun_app$b'('fmb_A_bool_fun$_1','fmb_A$_2') 3.02/0.88 & ~'fun_app$b'('fmb_A_bool_fun$_2','fmb_A$_1') 3.02/0.88 & ~'fun_app$b'('fmb_A_bool_fun$_2','fmb_A$_2') 3.02/0.88 & ~'fun_app$b'('fmb_A_bool_fun$_3','fmb_A$_1') 3.02/0.88 & ~'fun_app$b'('fmb_A_bool_fun$_3','fmb_A$_2') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_less_eq$',type,'less_eq$': ('A_n_vec_set$' * 'A_n_vec_set$') > $o). 3.02/0.88 tff('predicate_less_eq$',axiom, 3.02/0.88 ~'less_eq$'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set$_1') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_fun_app$a',type,'fun_app$a': ('A_n_vec_bool_fun$' * 'A_n_vec$') > $o). 3.02/0.88 tff('predicate_fun_app$a',axiom, 3.02/0.88 ~'fun_app$a'('fmb_A_n_vec_bool_fun$_1','fmb_A_n_vec$_1') 3.02/0.88 & ~'fun_app$a'('fmb_A_n_vec_bool_fun$_1','fmb_A_n_vec$_2') 3.02/0.88 & ~'fun_app$a'('fmb_A_n_vec_bool_fun$_2','fmb_A_n_vec$_1') 3.02/0.88 & ~'fun_app$a'('fmb_A_n_vec_bool_fun$_2','fmb_A_n_vec$_2') 3.02/0.88 & ~'fun_app$a'('fmb_A_n_vec_bool_fun$_3','fmb_A_n_vec$_1') 3.02/0.88 & ~'fun_app$a'('fmb_A_n_vec_bool_fun$_3','fmb_A_n_vec$_2') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_invertible$a',type,'invertible$a': ('A_n_vec_n_vec_n_vec$') > $o). 3.02/0.88 tff('predicate_invertible$a',axiom, 3.02/0.88 ~'invertible$a'('fmb_A_n_vec_n_vec_n_vec$_1') 3.02/0.88 & ~'invertible$a'('fmb_A_n_vec_n_vec_n_vec$_2') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_less_eq$a',type,'less_eq$a': ('A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$') > $o). 3.02/0.88 tff('predicate_less_eq$a',axiom, 3.02/0.88 'less_eq$a'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_1') 3.02/0.88 & ~'less_eq$a'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_2') 3.02/0.88 & 'less_eq$a'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_3') 3.02/0.88 & ~'less_eq$a'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_1') 3.02/0.88 & 'less_eq$a'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_2') 3.02/0.88 & 'less_eq$a'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_3') 3.02/0.88 & ~'less_eq$a'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_1') 3.02/0.88 & ~'less_eq$a'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_2') 3.02/0.88 & 'less_eq$a'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_3') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_less_eq$b',type,'less_eq$b': ('A_set$' * 'A_set$') > $o). 3.02/0.88 tff('predicate_less_eq$b',axiom, 3.02/0.88 ~'less_eq$b'('fmb_A_set$_1','fmb_A_set$_1') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_member$c',type,'member$c': ('A_set$' * 'A_set_set$') > $o). 3.02/0.88 tff('predicate_member$c',axiom, 3.02/0.88 ~'member$c'('fmb_A_set$_1','fmb_A_set_set$_1') 3.02/0.88 & ~'member$c'('fmb_A_set$_1','fmb_A_set_set$_2') 3.02/0.88 & ~'member$c'('fmb_A_set$_1','fmb_A_set_set$_3') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_member$a',type,'member$a': ('A_n_vec$' * 'A_n_vec_set$') > $o). 3.02/0.88 tff('predicate_member$a',axiom, 3.02/0.88 ~'member$a'('fmb_A_n_vec$_1','fmb_A_n_vec_set$_1') 3.02/0.88 & ~'member$a'('fmb_A_n_vec$_2','fmb_A_n_vec_set$_1') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 tff('declare_fun_app$',type,'fun_app$': ('A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec$') > $o). 3.02/0.88 tff('predicate_fun_app$',axiom, 3.02/0.88 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_1','fmb_A_n_vec_n_vec$_1') 3.02/0.88 & ~'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_1','fmb_A_n_vec_n_vec$_2') 3.02/0.88 & 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_2','fmb_A_n_vec_n_vec$_1') 3.02/0.88 & 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_2','fmb_A_n_vec_n_vec$_2') 3.02/0.88 & ~'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_3','fmb_A_n_vec_n_vec$_1') 3.02/0.88 & 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_3','fmb_A_n_vec_n_vec$_2') 3.02/0.88 3.02/0.88 ). 3.02/0.88 3.02/0.88 % SZS output end FiniteModel for theBenchmark 3.02/0.88 % (5983)------------------------------ 3.02/0.88 % (5983)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 3.02/0.88 % (5983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.02/0.88 % (5983)Termination reason: Satisfiable 3.02/0.88 3.02/0.88 % (5983)Time elapsed: 0.441 s 3.02/0.88 % (5983)Peak memory usage: 23 MB 3.02/0.88 % (5983)Instructions burned: 1099 (million) 3.02/0.88 % (5983)------------------------------ 3.02/0.88 % (5983)------------------------------ 3.02/0.88 % (5981)Success in time 0.536 s 3.02/0.88 EOF