%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% 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 : 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 05:34:43 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_004,axiom,
! [X2,X3] : x2(s(X3),X2) = s(x2(X3,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(axiom_006,axiom,
! [X2,X3] : x22(s(X3),X2) = x2(X2,x22(X3,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(axiom_001,axiom,
! [X1] : proj1S(s(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(goal_007,conjecture,
? [X1] : x22(X1,X1) != X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_007) ).
fof(axiom_005,axiom,
! [X2] : x22(z,X2) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(axiom_003,axiom,
! [X2] : x2(z,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
fof(axiom_002,axiom,
! [X1] : z != s(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(c_0_7,plain,
! [X16,X17] : x2(s(X17),X16) = s(x2(X17,X16)),
inference(variable_rename,[status(thm)],[axiom_004]) ).
fof(c_0_8,plain,
! [X19,X20] : x22(s(X20),X19) = x2(X19,x22(X20,X19)),
inference(variable_rename,[status(thm)],[axiom_006]) ).
fof(c_0_9,plain,
! [X13] : proj1S(s(X13)) = X13,
inference(variable_rename,[status(thm)],[axiom_001]) ).
cnf(c_0_10,plain,
x2(s(X1),X2) = s(x2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
x22(s(X1),X2) = x2(X2,x22(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
~ ? [X1] : x22(X1,X1) != X1,
inference(assume_negation,[status(cth)],[goal_007]) ).
cnf(c_0_13,plain,
proj1S(s(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
s(x2(X1,x22(X2,s(X1)))) = x22(s(X2),s(X1)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_15,negated_conjecture,
! [X21] : x22(X21,X21) = X21,
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_16,plain,
! [X18] : x22(z,X18) = z,
inference(variable_rename,[status(thm)],[axiom_005]) ).
cnf(c_0_17,plain,
proj1S(x22(s(X1),s(X2))) = x2(X2,x22(X1,s(X2))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
x22(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
x22(z,X1) = z,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X15] : x2(z,X15) = X15,
inference(variable_rename,[status(thm)],[axiom_003]) ).
cnf(c_0_21,negated_conjecture,
x2(X1,x22(X1,s(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13]) ).
cnf(c_0_22,plain,
x22(s(z),X1) = x2(X1,z),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_23,plain,
x2(z,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X14] : z != s(X14),
inference(variable_rename,[status(thm)],[axiom_002]) ).
cnf(c_0_25,negated_conjecture,
s(s(s(z))) = s(z),
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_21,c_0_22]),c_0_10]),c_0_10]),c_0_23]),c_0_10]),c_0_23]) ).
cnf(c_0_26,plain,
z != s(X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_25]),c_0_13]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% 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
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 07:56:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------