%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX207+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 : n018.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 05:34:44 PM UTC 2026
% Result : Theorem 1.21s 1.66s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 20 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_027,conjecture,
? [X8,X9] :
~ ( linC(X8) = linC(X9)
=> X8 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_027) ).
fof(axiom_026,axiom,
! [X6,X7] : linC(c2(X6,X7)) = append(linP(X6),linP(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_019,axiom,
! [X3] : append(nil,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(axiom_025,axiom,
linP(pE) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(axiom_020,axiom,
! [X3,X4,X5] : append(cons(X4,X5),X3) = cons(X4,append(X5,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(axiom_017,axiom,
! [X1,X2] : proj1C(c2(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(axiom_024,axiom,
linP(pB) = cons(b,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(axiom_016,axiom,
pB != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(c_0_8,negated_conjecture,
~ ? [X8,X9] :
~ ( linC(X8) = linC(X9)
=> X8 = X9 ),
inference(assume_negation,[status(cth)],[goal_027]) ).
fof(c_0_9,negated_conjecture,
! [X68,X69] :
( linC(X68) != linC(X69)
| X68 = X69 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_10,plain,
! [X66,X67] : linC(c2(X66,X67)) = append(linP(X66),linP(X67)),
inference(variable_rename,[status(thm)],[axiom_026]) ).
cnf(c_0_11,negated_conjecture,
( X1 = X2
| linC(X1) != linC(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
linC(c2(X1,X2)) = append(linP(X1),linP(X2)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X60] : append(nil,X60) = X60,
inference(variable_rename,[status(thm)],[axiom_019]) ).
cnf(c_0_14,negated_conjecture,
( c2(X1,X2) = X3
| append(linP(X1),linP(X2)) != linC(X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
linP(pE) = nil,
inference(split_conjunct,[status(thm)],[axiom_025]) ).
cnf(c_0_16,plain,
append(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( c2(pE,X1) = X2
| linP(X1) != linC(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,negated_conjecture,
( c2(pE,X1) = c2(X2,X3)
| linP(X1) != append(linP(X2),linP(X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
fof(c_0_19,plain,
! [X61,X62,X63] : append(cons(X62,X63),X61) = cons(X62,append(X63,X61)),
inference(variable_rename,[status(thm)],[axiom_020]) ).
fof(c_0_20,plain,
! [X56,X57] : proj1C(c2(X56,X57)) = X56,
inference(variable_rename,[status(thm)],[axiom_017]) ).
cnf(c_0_21,negated_conjecture,
( c2(pE,X1) = c2(X2,pE)
| linP(X1) != append(linP(X2),nil) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_22,plain,
linP(pB) = cons(b,nil),
inference(split_conjunct,[status(thm)],[axiom_024]) ).
cnf(c_0_23,plain,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
proj1C(c2(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( c2(pE,X1) = c2(pB,pE)
| linP(X1) != cons(b,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_16]) ).
cnf(c_0_26,plain,
pB != pE,
inference(split_conjunct,[status(thm)],[axiom_016]) ).
cnf(c_0_27,negated_conjecture,
linP(X1) != cons(b,nil),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_24]),c_0_26]) ).
cnf(c_0_28,plain,
$false,
inference(sr,[status(thm)],[c_0_22,c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.09 % 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
% 0.10/0.28 % Computer : n018.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue May 5 07:56:47 EDT 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.29 % start to proof: theBenchmark
% 1.21/1.66 % Version : CSE_E---1.7
% 1.21/1.66 % Problem : theBenchmark.p
% 1.21/1.66 % SZS status Theorem for theBenchmark.p
% 1.21/1.66 % SZS output start CNFRefutation
% See solution above
% 1.21/1.66 % Total time : 1.367s
%------------------------------------------------------------------------------