%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LDA004-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 May 5 04:46:53 PM UTC 2026
% Result : Unsatisfiable 204.29s 108.65s
% Output : CNFRefutation 205.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 55 ( 50 unt; 0 nHn; 32 RR)
% Number of literals : 63 ( 40 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 49 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a2,axiom,
left(X1,f(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
cnf(a1,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
cnf(clause_7,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
cnf(a3,axiom,
( left(X1,X3)
| ~ left(X1,X2)
| ~ left(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
cnf(clause_10,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
cnf(clause_8,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
cnf(clause_5,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
cnf(clause_9,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
cnf(clause_4,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
cnf(clause_6,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
cnf(clause_11,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
cnf(prove_equation,negated_conjecture,
~ left(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_12,axiom,
left(X1,f(X1,X2)),
a2 ).
cnf(c_0_13,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
a1 ).
cnf(c_0_14,axiom,
u1 = f(u,n1),
clause_7 ).
cnf(c_0_15,axiom,
( left(X1,X3)
| ~ left(X1,X2)
| ~ left(X2,X3) ),
a3 ).
cnf(c_0_16,plain,
left(f(X1,X2),f(X1,f(X2,X3))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
a = f(f(n3,n2),u2),
clause_10 ).
cnf(c_0_18,plain,
f(f(u,X1),u1) = f(u,f(X1,n1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,axiom,
u2 = f(u,n2),
clause_8 ).
cnf(c_0_20,axiom,
n3 = f(n2,n1),
clause_5 ).
cnf(c_0_21,axiom,
u3 = f(u,n3),
clause_9 ).
cnf(c_0_22,axiom,
n2 = f(n1,n1),
clause_4 ).
cnf(c_0_23,plain,
( left(X1,f(X2,X3))
| ~ left(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_24,plain,
left(a,f(f(n3,n2),f(u2,X1))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
f(u2,u1) = u3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
f(f(n1,X1),n2) = f(n1,f(X1,n1)),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_27,axiom,
u = f(n2,n2),
clause_6 ).
cnf(c_0_28,plain,
( left(X1,f(X2,X3))
| ~ left(X1,X4)
| ~ left(X4,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_29,plain,
left(a,f(f(n3,n2),u3)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
f(f(u,X1),u2) = f(u,f(X1,n2)),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_31,plain,
f(f(n2,X1),n3) = f(n2,f(X1,n1)),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_32,plain,
f(n1,n2) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_27]),c_0_22]) ).
cnf(c_0_33,plain,
f(f(n2,X1),u) = f(n2,f(X1,n2)),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_34,plain,
( left(a,f(X1,X2))
| ~ left(f(f(n3,n2),u3),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
f(f(X1,f(X2,X3)),f(f(X1,X2),X4)) = f(f(X1,X2),f(f(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_36,plain,
f(u,f(n3,n2)) = f(u3,u2),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_37,plain,
f(n3,n3) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_20]),c_0_22]),c_0_27]) ).
cnf(c_0_38,plain,
f(n3,f(n2,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_39,plain,
f(n2,n3) = u3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_21]),c_0_20]) ).
cnf(c_0_40,plain,
f(n1,n3) = u2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_32]),c_0_19]),c_0_20]) ).
cnf(c_0_41,plain,
f(u,u) = f(n2,u),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_27]),c_0_27]) ).
cnf(c_0_42,plain,
left(a,f(f(f(n3,n2),f(u3,X1)),X2)),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_43,plain,
f(f(X1,f(u3,u2)),f(f(X1,u),X2)) = f(f(X1,u),f(f(X1,f(n3,n2)),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
f(f(n3,X1),u) = f(n3,f(X1,n3)),
inference(spm,[status(thm)],[c_0_13,c_0_37]) ).
cnf(c_0_45,plain,
f(n3,u3) = f(n2,u2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_46,plain,
f(n3,u) = f(n2,u),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_32]) ).
cnf(c_0_47,plain,
f(f(X1,u2),f(f(X1,u),X2)) = f(f(X1,u),f(f(X1,n2),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_19]) ).
cnf(c_0_48,plain,
f(f(n2,u),f(u,X1)) = f(u,f(u,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_41]) ).
cnf(c_0_49,plain,
f(f(u,X1),u3) = f(u,f(X1,n3)),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_50,axiom,
b = f(u1,u3),
clause_11 ).
cnf(c_0_51,plain,
left(a,f(u,f(u,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_39]),c_0_45]),c_0_13]),c_0_27]),c_0_46]),c_0_47]),c_0_27]),c_0_48]) ).
cnf(c_0_52,plain,
f(u,u2) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_14]),c_0_50]),c_0_40]) ).
cnf(c_0_53,negated_conjecture,
~ left(a,b),
prove_equation ).
cnf(c_0_54,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_19]),c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LDA004-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 23:19:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 204.29/108.65 % Version : CSE_E---1.7
% 204.29/108.65 % Problem : theBenchmark.p
% 204.29/108.65 % SZS status Unsatisfiable for theBenchmark.p
% 204.29/108.65 % SZS output start CNFRefutation
% See solution above
% 205.72/110.07 % Total time : 75.909s
%------------------------------------------------------------------------------