%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LDA002-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 04:46:52 PM UTC 2026
% Result : Unsatisfiable 1.35s 1.76s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 47 RR)
% Number of literals : 62 ( 61 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
cnf(clause_7,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
cnf(clause_4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
cnf(clause_6,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
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_3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
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_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,
n2 = f(n1,n1),
clause_2 ).
cnf(c_0_14,axiom,
u3 = f(u,n3),
clause_7 ).
cnf(c_0_15,plain,
f(f(n1,X1),n2) = f(n1,f(X1,n1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
u = f(n2,n2),
clause_4 ).
cnf(c_0_17,axiom,
u2 = f(u,n2),
clause_6 ).
cnf(c_0_18,plain,
f(f(u,X1),u3) = f(u,f(X1,n3)),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_19,axiom,
u1 = f(u,n1),
clause_5 ).
cnf(c_0_20,axiom,
b = f(u1,u3),
clause_10 ).
cnf(c_0_21,plain,
f(n1,n2) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_16]),c_0_13]) ).
cnf(c_0_22,axiom,
n3 = f(n2,n1),
clause_3 ).
cnf(c_0_23,axiom,
uu = f(u,u),
clause_8 ).
cnf(c_0_24,plain,
f(f(u,X1),u2) = f(u,f(X1,n2)),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_25,plain,
f(u,f(n1,n3)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_26,plain,
f(n1,n3) = u2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_17]),c_0_22]) ).
cnf(c_0_27,plain,
f(f(u,X1),uu) = f(u,f(X1,u)),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_28,axiom,
v = f(uu,uu),
clause_11 ).
cnf(c_0_29,plain,
f(f(n2,X1),u) = f(n2,f(X1,n2)),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_30,plain,
f(uu,u2) = f(u,u2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_17]) ).
cnf(c_0_31,plain,
f(u,u2) = b,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
f(u,uu) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_28]),c_0_23]) ).
cnf(c_0_33,plain,
f(f(uu,X1),v) = f(uu,f(X1,uu)),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_34,axiom,
a = f(f(n3,n2),u2),
clause_9 ).
cnf(c_0_35,plain,
f(n2,u) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_23]),c_0_16]) ).
cnf(c_0_36,plain,
f(n1,f(n1,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_37,plain,
f(uu,u2) = b,
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
f(u,f(n2,u)) = f(u2,uu),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_39,plain,
f(v,f(u,X1)) = f(u,f(uu,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_32]) ).
cnf(c_0_40,plain,
f(v,v) = f(uu,v),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_28]) ).
cnf(c_0_41,plain,
f(f(f(n3,n2),X1),a) = f(f(n3,n2),f(X1,u2)),
inference(spm,[status(thm)],[c_0_12,c_0_34]) ).
cnf(c_0_42,plain,
f(u2,u2) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_16]),c_0_23]) ).
cnf(c_0_43,plain,
f(n3,u) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_21]),c_0_35]) ).
cnf(c_0_44,plain,
f(n3,f(n2,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_45,plain,
f(n1,u) = uu,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_21]),c_0_35]) ).
cnf(c_0_46,plain,
f(u,f(n2,X1)) = f(n2,f(n2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_47,plain,
f(uu,f(u2,uu)) = f(b,v),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_48,plain,
f(u2,uu) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_35]),c_0_32]) ).
cnf(c_0_49,plain,
f(uu,v) = f(u,v),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_40]),c_0_28]) ).
cnf(c_0_50,plain,
f(f(n3,n2),uu) = f(a,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_34]),c_0_42]) ).
cnf(c_0_51,plain,
f(f(n3,X1),uu) = f(n3,f(X1,u)),
inference(spm,[status(thm)],[c_0_12,c_0_43]) ).
cnf(c_0_52,plain,
f(n3,uu) = f(n2,uu),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_45]) ).
cnf(c_0_53,plain,
f(n2,uu) = v,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_35]),c_0_32]) ).
cnf(c_0_54,negated_conjecture,
f(a,v) != f(b,v),
prove_equation ).
cnf(c_0_55,plain,
f(b,v) = f(u,v),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_56,plain,
f(a,a) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_35]),c_0_52]),c_0_53]) ).
cnf(c_0_57,negated_conjecture,
f(a,v) != f(u,v),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,plain,
f(u,v) = f(n2,v),
inference(spm,[status(thm)],[c_0_46,c_0_53]) ).
cnf(c_0_59,plain,
f(a,f(a,X1)) = f(v,f(a,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
f(a,v) != f(n2,v),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_40]),c_0_49]),c_0_58]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LDA002-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n021.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 23:20:40 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.35/1.76 % Version : CSE_E---1.7
% 1.35/1.76 % Problem : theBenchmark.p
% 1.35/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.35/1.76 % SZS output start CNFRefutation
% See solution above
% 1.35/1.77 % Total time : 1.370s
%------------------------------------------------------------------------------