TSTP Solution File: COL121-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : COL121-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:35:10 EDT 2023
% Result : Unsatisfiable 15.19s 6.29s
% Output : CNFRefutation 15.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 44 ( 7 unt; 13 typ; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 49 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 7 >; 11 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 58 (; 58 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_Comb_Odiamond > c_Pair > c_Comb_Odiamond__strip__lemmaE__1 > tc_prod > c_Transitive__Closure_Ortrancl > #nlpp > v_x > v_z > v_ya > v_y > v_xaa > v_r > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(v_y,type,
v_y: $i ).
tff(t_a,type,
t_a: $i ).
tff(v_z,type,
v_z: $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(v_ya,type,
v_ya: $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_xaa,type,
v_xaa: $i ).
tff(v_r,type,
v_r: $i ).
tff(c_Comb_Odiamond,type,
c_Comb_Odiamond: ( $i * $i ) > $o ).
tff(c_Pair,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(c_Comb_Odiamond__strip__lemmaE__1,type,
c_Comb_Odiamond__strip__lemmaE__1: ( $i * $i * $i * $i ) > $i ).
tff(v_x,type,
v_x: $i > $i ).
tff(f_63,axiom,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file(unknown,unknown) ).
tff(f_62,axiom,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file(unknown,unknown) ).
tff(f_61,axiom,
c_Comb_Odiamond(v_r,t_a),
file(unknown,unknown) ).
tff(f_68,axiom,
! [V_U] :
( c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [V_r,T_a,V_y,V_x,V_y_H] :
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [V_p,V_r,T_a] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [V_U] :
( c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [V_r,V_a,T_a,V_c,V_b] :
( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [V_r,T_a,V_y,V_x,V_y_H] :
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [V_U] :
( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(c_14,plain,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_12,plain,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_10,plain,
c_Comb_Odiamond(v_r,t_a),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_16,plain,
! [V_U_19] :
( ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(V_U_19),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_74,plain,
! [V_x_38,V_y_H_40,V_y_37,V_r_39,T_a_36] :
( c_in(c_Pair(V_y_37,c_Comb_Odiamond__strip__lemmaE__1(V_r_39,V_y_37,V_y_H_40,T_a_36),T_a_36,T_a_36),V_r_39,tc_prod(T_a_36,T_a_36))
| ~ c_in(c_Pair(V_x_38,V_y_37,T_a_36,T_a_36),c_Transitive__Closure_Ortrancl(V_r_39,T_a_36),tc_prod(T_a_36,T_a_36))
| ~ c_in(c_Pair(V_x_38,V_y_H_40,T_a_36,T_a_36),V_r_39,tc_prod(T_a_36,T_a_36))
| ~ c_Comb_Odiamond(V_r_39,T_a_36) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_80,plain,
! [V_U_19,V_y_H_40] :
( c_in(c_Pair(v_x(V_U_19),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_19),V_y_H_40,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,V_y_H_40,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_16,c_74]) ).
tff(c_94,plain,
! [V_U_19,V_y_H_40] :
( c_in(c_Pair(v_x(V_U_19),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_19),V_y_H_40,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,V_y_H_40,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_80]) ).
tff(c_6,plain,
! [V_p_11,V_r_12,T_a_13] :
( c_in(V_p_11,c_Transitive__Closure_Ortrancl(V_r_12,T_a_13),tc_prod(T_a_13,T_a_13))
| ~ c_in(V_p_11,V_r_12,tc_prod(T_a_13,T_a_13)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_18,plain,
! [V_U_20] :
( ~ c_in(c_Pair(v_y,V_U_20,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(V_U_20,v_x(V_U_20),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_47,plain,
! [V_r_34,V_a_30,T_a_33,V_b_31,V_c_32] :
( c_in(c_Pair(V_a_30,V_c_32,T_a_33,T_a_33),c_Transitive__Closure_Ortrancl(V_r_34,T_a_33),tc_prod(T_a_33,T_a_33))
| ~ c_in(c_Pair(V_a_30,V_b_31,T_a_33,T_a_33),c_Transitive__Closure_Ortrancl(V_r_34,T_a_33),tc_prod(T_a_33,T_a_33))
| ~ c_in(c_Pair(V_b_31,V_c_32,T_a_33,T_a_33),c_Transitive__Closure_Ortrancl(V_r_34,T_a_33),tc_prod(T_a_33,T_a_33)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_466,plain,
! [V_U_76,V_c_77] :
( c_in(c_Pair(V_U_76,V_c_77,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(V_U_76),V_c_77,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U_76,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_18,c_47]) ).
tff(c_770,plain,
! [V_U_100,V_c_101] :
( c_in(c_Pair(V_U_100,V_c_101,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U_100,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(V_U_100),V_c_101,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_6,c_466]) ).
tff(c_25189,plain,
! [V_U_500,V_y_H_501] :
( c_in(c_Pair(V_U_500,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_500),V_y_H_501,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,V_y_H_501,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U_500,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_94,c_770]) ).
tff(c_104,plain,
! [V_y_H_44,T_a_42,V_r_43,V_x_46,V_y_45] :
( c_in(c_Pair(V_y_H_44,c_Comb_Odiamond__strip__lemmaE__1(V_r_43,V_y_45,V_y_H_44,T_a_42),T_a_42,T_a_42),c_Transitive__Closure_Ortrancl(V_r_43,T_a_42),tc_prod(T_a_42,T_a_42))
| ~ c_in(c_Pair(V_x_46,V_y_45,T_a_42,T_a_42),c_Transitive__Closure_Ortrancl(V_r_43,T_a_42),tc_prod(T_a_42,T_a_42))
| ~ c_in(c_Pair(V_x_46,V_y_H_44,T_a_42,T_a_42),V_r_43,tc_prod(T_a_42,T_a_42))
| ~ c_Comb_Odiamond(V_r_43,T_a_42) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_110,plain,
! [V_y_H_44,V_U_19] :
( c_in(c_Pair(V_y_H_44,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_19),V_y_H_44,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,V_y_H_44,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_y,V_U_19,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_16,c_104]) ).
tff(c_1317,plain,
! [V_y_H_129,V_U_130] :
( c_in(c_Pair(V_y_H_129,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_130),V_y_H_129,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,V_y_H_129,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U_130,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_110]) ).
tff(c_20,plain,
! [V_U_21] :
( ~ c_in(c_Pair(v_z,V_U_21,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U_21,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1360,plain,
! [V_U_130] :
( ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_130),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U_130,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_1317,c_20]) ).
tff(c_1382,plain,
! [V_U_130] :
( ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(V_U_130),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U_130,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1360]) ).
tff(c_25355,plain,
( ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_25189,c_1382]) ).
tff(c_25519,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_12,c_25355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COL121-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.30 % Computer : n003.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Aug 3 18:18:38 EDT 2023
% 0.09/0.30 % CPUTime :
% 15.19/6.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.19/6.30
% 15.19/6.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.30/6.33
% 15.30/6.33 Inference rules
% 15.30/6.33 ----------------------
% 15.30/6.33 #Ref : 0
% 15.30/6.33 #Sup : 6007
% 15.30/6.33 #Fact : 0
% 15.30/6.33 #Define : 0
% 15.30/6.33 #Split : 43
% 15.30/6.33 #Chain : 0
% 15.30/6.33 #Close : 0
% 15.30/6.33
% 15.30/6.33 Ordering : KBO
% 15.30/6.33
% 15.30/6.33 Simplification rules
% 15.30/6.33 ----------------------
% 15.30/6.33 #Subsume : 2171
% 15.30/6.33 #Demod : 1165
% 15.30/6.33 #Tautology : 225
% 15.30/6.33 #SimpNegUnit : 1
% 15.30/6.33 #BackRed : 0
% 15.30/6.33
% 15.30/6.33 #Partial instantiations: 0
% 15.30/6.33 #Strategies tried : 1
% 15.30/6.33
% 15.30/6.33 Timing (in seconds)
% 15.30/6.33 ----------------------
% 15.30/6.33 Preprocessing : 0.46
% 15.30/6.33 Parsing : 0.26
% 15.30/6.33 CNF conversion : 0.02
% 15.30/6.33 Main loop : 4.96
% 15.30/6.33 Inferencing : 1.21
% 15.30/6.33 Reduction : 1.27
% 15.30/6.33 Demodulation : 0.87
% 15.30/6.33 BG Simplification : 0.07
% 15.30/6.33 Subsumption : 2.13
% 15.30/6.33 Abstraction : 0.10
% 15.30/6.33 MUC search : 0.00
% 15.30/6.33 Cooper : 0.00
% 15.30/6.33 Total : 5.47
% 15.30/6.33 Index Insertion : 0.00
% 15.30/6.33 Index Deletion : 0.00
% 15.30/6.33 Index Matching : 0.00
% 15.30/6.33 BG Taut test : 0.00
%------------------------------------------------------------------------------