%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 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 : 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 05:34:43 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.71s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 5 RR)
% Number of literals : 25 ( 24 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_001,axiom,
x2(s(X1),X2) = s(x2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_003,axiom,
x22(s(X1),X2) = x2(X2,x22(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom,axiom,
x2(z,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_002,axiom,
x22(z,X1) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
cnf(goal,negated_conjecture,
eq2(mul_idem(X1),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(axiom_004,axiom,
mul_idem(X1) = eq(x22(X1,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_007,axiom,
eq(s(X1),s(X2)) = eq(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_009,axiom,
eq(s(X1),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom_011,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
cnf(c_0_9,axiom,
x2(s(X1),X2) = s(x2(X1,X2)),
axiom_001 ).
cnf(c_0_10,axiom,
x22(s(X1),X2) = x2(X2,x22(X1,X2)),
axiom_003 ).
cnf(c_0_11,plain,
s(x2(X1,x22(X2,s(X1)))) = x22(s(X2),s(X1)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
s(s(x2(X1,x22(X2,s(s(X1)))))) = x22(s(X2),s(s(X1))),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_13,axiom,
x2(z,X1) = X1,
axiom ).
cnf(c_0_14,axiom,
x22(z,X1) = z,
axiom_002 ).
cnf(c_0_15,negated_conjecture,
eq2(mul_idem(X1),bfalse) != btrue,
goal ).
cnf(c_0_16,axiom,
mul_idem(X1) = eq(x22(X1,X1),X1),
axiom_004 ).
cnf(c_0_17,plain,
s(s(x22(X1,s(s(z))))) = x22(s(X1),s(s(z))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
x22(s(z),X1) = x2(X1,z),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
eq2(eq(x22(X1,X1),X1),bfalse) != btrue,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_9]),c_0_9]),c_0_13]) ).
cnf(c_0_21,axiom,
eq(s(X1),s(X2)) = eq(X1,X2),
axiom_007 ).
cnf(c_0_22,axiom,
eq(s(X1),z) = bfalse,
axiom_009 ).
cnf(c_0_23,axiom,
eq2(X1,X1) = btrue,
axiom_011 ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_21]),c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 07:57:11 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.27/1.71 % Version : CSE_E---1.7
% 1.27/1.71 % Problem : theBenchmark.p
% 1.27/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.71 % SZS output start CNFRefutation
% See solution above
% 1.27/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------