%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX190+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 : n017.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 05:34:40 PM UTC 2026
% Result : Theorem 1.37s 1.75s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 33 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 12 ~; 4 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 56 ( 14 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_054,conjecture,
? [X6] : opt(d(X6)) != opt(d(opt(X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_054) ).
fof(axiom_053,axiom,
! [X12] : opt(y(n(z),X12)) = n(z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_053) ).
fof(axiom_039,axiom,
! [X5] : d(n(X5)) = n(z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_039) ).
fof(axiom_009,axiom,
! [X1,X2,X3] : n(X1) != y(X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(axiom_047,axiom,
! [X1] :
( X1 != x(proj1(X1),proj2(X1))
=> ( X1 != y(proj12(X1),proj22(X1))
=> opt(X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_047) ).
fof(axiom_008,axiom,
! [X1,X2,X3] : n(X1) != x(X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_050,axiom,
! [X6] : opt(x(n(z),X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_050) ).
fof(axiom_040,axiom,
! [X20,X21] : d(x(X20,X21)) = x(d(X20),d(X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_040) ).
fof(axiom_041,axiom,
! [X22,X23] : d(y(X22,X23)) = x(y(d(X22),X23),y(X22,d(X23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_041) ).
fof(c_0_9,negated_conjecture,
~ ? [X6] : opt(d(X6)) != opt(d(opt(X6))),
inference(assume_negation,[status(cth)],[goal_054]) ).
fof(c_0_10,negated_conjecture,
! [X215] : opt(d(X215)) = opt(d(opt(X215))),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_11,plain,
! [X214] : opt(y(n(z),X214)) = n(z),
inference(variable_rename,[status(thm)],[axiom_053]) ).
fof(c_0_12,plain,
! [X193] : d(n(X193)) = n(z),
inference(variable_rename,[status(thm)],[axiom_039]) ).
fof(c_0_13,plain,
! [X135,X136,X137] : n(X135) != y(X136,X137),
inference(variable_rename,[status(thm)],[axiom_009]) ).
fof(c_0_14,plain,
! [X204] :
( X204 = x(proj1(X204),proj2(X204))
| X204 = y(proj12(X204),proj22(X204))
| opt(X204) = X204 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_047])]) ).
fof(c_0_15,plain,
! [X132,X133,X134] : n(X132) != x(X133,X134),
inference(variable_rename,[status(thm)],[axiom_008]) ).
fof(c_0_16,plain,
! [X209] : opt(x(n(z),X209)) = X209,
inference(variable_rename,[status(thm)],[axiom_050]) ).
fof(c_0_17,plain,
! [X194,X195] : d(x(X194,X195)) = x(d(X194),d(X195)),
inference(variable_rename,[status(thm)],[axiom_040]) ).
cnf(c_0_18,negated_conjecture,
opt(d(X1)) = opt(d(opt(X1))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
opt(y(n(z),X1)) = n(z),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
d(n(X1)) = n(z),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
n(X1) != y(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( X1 = x(proj1(X1),proj2(X1))
| X1 = y(proj12(X1),proj22(X1))
| opt(X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
n(X1) != x(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
opt(x(n(z),X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
d(x(X1,X2)) = x(d(X1),d(X2)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_26,plain,
! [X196,X197] : d(y(X196,X197)) = x(y(d(X196),X197),y(X196,d(X197))),
inference(variable_rename,[status(thm)],[axiom_041]) ).
cnf(c_0_27,negated_conjecture,
opt(d(y(n(z),X1))) = opt(n(z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_28,plain,
opt(n(X1)) = n(X1),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
opt(d(x(n(z),X1))) = opt(d(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_30,plain,
d(x(n(X1),X2)) = x(n(z),d(X2)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_31,plain,
d(y(X1,X2)) = x(y(d(X1),X2),y(X1,d(X2))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
opt(d(y(n(z),X1))) = n(z),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
opt(d(X1)) = d(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_24]) ).
cnf(c_0_34,plain,
n(X1) != d(y(X2,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX190+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 : n017.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 07:52:27 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.37/1.75 % Version : CSE_E---1.7
% 1.37/1.75 % Problem : theBenchmark.p
% 1.37/1.75 % SZS status Theorem for theBenchmark.p
% 1.37/1.75 % SZS output start CNFRefutation
% See solution above
% 1.37/1.76 % Total time : 1.374s
%------------------------------------------------------------------------------