TSTP Solution File: LDA002-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 : Thu Aug 31 09:03:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 73 ( 61 unt; 12 typ; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
f: ( $i * $i ) > $i ).
tff(decl_23,type,
n2: $i ).
tff(decl_24,type,
n1: $i ).
tff(decl_25,type,
n3: $i ).
tff(decl_26,type,
u: $i ).
tff(decl_27,type,
u1: $i ).
tff(decl_28,type,
u2: $i ).
tff(decl_29,type,
u3: $i ).
tff(decl_30,type,
uu: $i ).
tff(decl_31,type,
a: $i ).
tff(decl_32,type,
b: $i ).
tff(decl_33,type,
v: $i ).
cnf(a1,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
cnf(clause_8,axiom,
uu = f(u,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
cnf(clause_11,axiom,
v = f(uu,uu),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
cnf(clause_7,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
cnf(clause_2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
cnf(clause_4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
cnf(clause_5,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
cnf(clause_10,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
cnf(clause_6,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
cnf(clause_3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
cnf(clause_9,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
cnf(prove_equation,negated_conjecture,
f(a,v) != f(b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_12,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
a1 ).
cnf(c_0_13,axiom,
uu = f(u,u),
clause_8 ).
cnf(c_0_14,plain,
f(f(u,X1),uu) = f(u,f(X1,u)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
v = f(uu,uu),
clause_11 ).
cnf(c_0_16,axiom,
u3 = f(u,n3),
clause_7 ).
cnf(c_0_17,axiom,
n2 = f(n1,n1),
clause_2 ).
cnf(c_0_18,axiom,
u = f(n2,n2),
clause_4 ).
cnf(c_0_19,plain,
f(u,uu) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15]),c_0_13]) ).
cnf(c_0_20,plain,
f(f(u,X1),u3) = f(u,f(X1,n3)),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_21,axiom,
u1 = f(u,n1),
clause_5 ).
cnf(c_0_22,axiom,
b = f(u1,u3),
clause_10 ).
cnf(c_0_23,plain,
f(f(n1,X1),n2) = f(n1,f(X1,n1)),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_24,axiom,
u2 = f(u,n2),
clause_6 ).
cnf(c_0_25,plain,
f(f(n2,X1),u) = f(n2,f(X1,n2)),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_26,plain,
f(f(u,X1),v) = f(u,f(X1,uu)),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_27,plain,
f(u,f(n1,n3)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,plain,
f(n1,n2) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_18]),c_0_17]) ).
cnf(c_0_29,axiom,
n3 = f(n2,n1),
clause_3 ).
cnf(c_0_30,axiom,
a = f(f(n3,n2),u2),
clause_9 ).
cnf(c_0_31,plain,
f(f(u,X1),u2) = f(u,f(X1,n2)),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_32,plain,
f(n2,u) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_13]),c_0_18]) ).
cnf(c_0_33,plain,
f(n1,f(n1,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_34,plain,
f(u,f(f(n1,n3),uu)) = f(b,v),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
f(n1,n3) = u2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_24]),c_0_29]) ).
cnf(c_0_36,plain,
f(u,f(n2,u)) = f(u2,uu),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_37,plain,
f(f(f(n3,n2),X1),a) = f(f(n3,n2),f(X1,u2)),
inference(spm,[status(thm)],[c_0_12,c_0_30]) ).
cnf(c_0_38,plain,
f(u2,u2) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_24]),c_0_18]),c_0_13]) ).
cnf(c_0_39,plain,
f(n3,u) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_28]),c_0_32]) ).
cnf(c_0_40,plain,
f(n3,f(n2,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_29]) ).
cnf(c_0_41,plain,
f(n1,u) = uu,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_32]) ).
cnf(c_0_42,plain,
f(u,f(n2,X1)) = f(n2,f(n2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_43,plain,
f(u,f(u2,uu)) = f(b,v),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,plain,
f(u2,uu) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_32]),c_0_19]) ).
cnf(c_0_45,plain,
f(f(n3,n2),uu) = f(a,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_38]) ).
cnf(c_0_46,plain,
f(f(n3,X1),uu) = f(n3,f(X1,u)),
inference(spm,[status(thm)],[c_0_12,c_0_39]) ).
cnf(c_0_47,plain,
f(n3,uu) = f(n2,uu),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_41]) ).
cnf(c_0_48,plain,
f(n2,uu) = v,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_19]) ).
cnf(c_0_49,plain,
f(f(uu,X1),v) = f(uu,f(X1,uu)),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_50,negated_conjecture,
f(a,v) != f(b,v),
prove_equation ).
cnf(c_0_51,plain,
f(b,v) = f(u,v),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
f(a,a) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_32]),c_0_47]),c_0_48]) ).
cnf(c_0_53,plain,
f(v,f(u,X1)) = f(u,f(uu,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_54,plain,
f(v,v) = f(uu,v),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_15]),c_0_15]) ).
cnf(c_0_55,negated_conjecture,
f(a,v) != f(u,v),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
f(u,v) = f(n2,v),
inference(spm,[status(thm)],[c_0_42,c_0_48]) ).
cnf(c_0_57,plain,
f(a,f(a,X1)) = f(v,f(a,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_52]) ).
cnf(c_0_58,plain,
f(uu,v) = f(u,v),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_19]),c_0_54]),c_0_15]) ).
cnf(c_0_59,negated_conjecture,
f(a,v) != f(n2,v),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_52]),c_0_54]),c_0_58]),c_0_56]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 01:04:49 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.050000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.053000 s
%------------------------------------------------------------------------------