%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC038-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:05:10 PM UTC 2026
% Result : Unsatisfiable 21.24s 3.16s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 25
% Syntax : Number of formulae : 165 ( 105 unt; 0 def)
% Number of atoms : 337 ( 134 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 394 ( 222 ~; 172 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 142 ( 2 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f114,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f114_nnf,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(t150,plain,
ifeq(X1,X2,ifeq(neq(X1,X2),true,ifeq(ssList(X2),true,ifeq(ssList(X1),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(t279,plain,
ifeq(X1,X2,ifeq(neq(X1,X2),true,ifeq(ssList(X2),true,ifeq(ssList(X1),true,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t150]) ).
cnf(f195,negated_conjecture,
( neq(sk3,nil)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f195_nnf,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(t76,plain,
or(eq(nil,sk3),neq(sk3,nil)) = true,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(f189,negated_conjecture,
nil = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f189_nnf,plain,
nil = sk2,
inference(nnf_transformation,[status(thm)],[f189]) ).
cnf(c189,plain,
nil = sk2,
inference(cnf_transformation,[status(esa)],[f189_nnf]) ).
cnf(t0,plain,
sk2 = nil,
inference(equality_encoding,[status(esa)],[c189]) ).
cnf(t577,plain,
nil = sk2,
inference(orient,[status(thm)],[t0]) ).
cnf(t9678,plain,
or(eq(sk2,sk3),neq(sk3,nil)) = true,
inference(step,[status(thm)],[t76,t577]) ).
cnf(t9679,plain,
or(eq(sk2,sk3),neq(sk3,sk2)) = true,
inference(step,[status(thm)],[t9678,t577]) ).
cnf(t634,plain,
or(eq(sk2,sk3),neq(sk3,sk2)) = true,
inference(orient,[status(thm)],[t9679]) ).
cnf(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f190_nnf,plain,
sk2 = sk4,
inference(nnf_transformation,[status(thm)],[f190]) ).
cnf(c190,plain,
sk2 = sk4,
inference(cnf_transformation,[status(esa)],[f190_nnf]) ).
cnf(t2,plain,
sk4 = sk2,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t672,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t2]) ).
cnf(t9691,plain,
or(eq(sk4,sk3),neq(sk3,sk2)) = true,
inference(step,[status(thm)],[t634,t672]) ).
cnf(t9692,plain,
or(eq(sk4,sk3),neq(sk3,sk4)) = true,
inference(step,[status(thm)],[t9691,t672]) ).
cnf(t677,plain,
or(eq(sk4,sk3),neq(sk3,sk4)) = true,
inference(rw,[status(thm)],[t9692]) ).
cnf(f192,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
nil != sk1,
inference(nnf_transformation,[status(thm)],[f192]) ).
fof(f192_sk,plain,
nil != sk1,
inference(skolemisation,[status(esa)],[f192_nnf]) ).
cnf(c192,plain,
nil != sk1,
inference(cnf_transformation,[status(esa)],[f192_sk]) ).
cnf(t21,plain,
eq(nil,sk1) = false,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t9683,plain,
eq(sk2,sk1) = false,
inference(step,[status(thm)],[t21,t577]) ).
cnf(t651,plain,
eq(sk2,sk1) = false,
inference(orient,[status(thm)],[t9683]) ).
cnf(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
sk1 = sk3,
inference(nnf_transformation,[status(thm)],[f191]) ).
cnf(c191,plain,
sk1 = sk3,
inference(cnf_transformation,[status(esa)],[f191_nnf]) ).
cnf(t1,plain,
sk3 = sk1,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t664,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t1]) ).
cnf(t9685,plain,
eq(sk2,sk3) = false,
inference(step,[status(thm)],[t651,t664]) ).
cnf(t665,plain,
eq(sk2,sk3) = false,
inference(rw,[status(thm)],[t9685]) ).
cnf(t9703,plain,
eq(sk4,sk3) = false,
inference(step,[status(thm)],[t665,t672]) ).
cnf(t6547,plain,
eq(sk4,sk3) = false,
inference(orient,[status(thm)],[t9703]) ).
cnf(t9919,plain,
or(false,neq(sk3,sk4)) = true,
inference(step,[status(thm)],[t677,t6547]) ).
cnf(t25,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t264,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t9920,plain,
neq(sk3,sk4) = true,
inference(step,[status(thm)],[t9919,t264]) ).
cnf(t8033,plain,
neq(sk3,sk4) = true,
inference(orient,[status(thm)],[t9920]) ).
cnf(t8037,plain,
true = ifeq(sk3,sk4,ifeq(true,true,ifeq(ssList(sk4),true,ifeq(ssList(sk3),true,false,true),true),true),true),
inference(cp,[status(thm)],[t279,t8033]) ).
cnf(t69,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t221,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t69]) ).
cnf(t9930,plain,
true = ifeq(sk3,sk4,ifeq(ssList(sk4),true,ifeq(ssList(sk3),true,false,true),true),true),
inference(step,[status(thm)],[t8037,t221]) ).
cnf(f7,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f7_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t11,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t9687,plain,
nil = sk4,
inference(step,[status(thm)],[t577,t672]) ).
cnf(t673,plain,
nil = sk4,
inference(orient,[status(thm)],[t9687]) ).
cnf(t9698,plain,
ssList(sk4) = true,
inference(step,[status(thm)],[t11,t673]) ).
cnf(t2356,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t9698]) ).
cnf(t9931,plain,
true = ifeq(sk3,sk4,ifeq(true,true,ifeq(ssList(sk3),true,false,true),true),true),
inference(step,[status(thm)],[t9930,t2356]) ).
cnf(t9932,plain,
true = ifeq(sk3,sk4,ifeq(ssList(sk3),true,false,true),true),
inference(step,[status(thm)],[t9931,t221]) ).
cnf(f187,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f187_nnf,plain,
ssList(sk3),
inference(nnf_transformation,[status(thm)],[f187]) ).
cnf(c187,plain,
ssList(sk3),
inference(cnf_transformation,[status(esa)],[f187_nnf]) ).
cnf(t14,plain,
ssList(sk3) = true,
inference(equality_encoding,[status(esa)],[c187]) ).
cnf(t2497,plain,
ssList(sk3) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t9933,plain,
true = ifeq(sk3,sk4,ifeq(true,true,false,true),true),
inference(step,[status(thm)],[t9932,t2497]) ).
cnf(t9934,plain,
true = ifeq(sk3,sk4,false,true),
inference(step,[status(thm)],[t9933,t221]) ).
cnf(t8046,plain,
ifeq(sk3,sk4,false,true) = true,
inference(orient,[status(thm)],[t9934]) ).
cnf(f128,axiom,
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
fof(f128_nnf,plain,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(nnf_transformation,[status(thm)],[f128]) ).
fof(f128_sk,plain,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(skolemisation,[status(esa)],[f128_nnf]) ).
cnf(c128,plain,
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f128_sk]) ).
cnf(t157,plain,
ifeq(frontsegP(X1,X2),true,ifeq(frontsegP(X2,X1),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,X2,X1),X1),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c128]) ).
cnf(t236,plain,
ifeq(frontsegP(X1,X2),true,ifeq(frontsegP(X2,X1),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,X2,X1),X1),X1),X1) = X1,
inference(orient,[status(thm)],[t157]) ).
cnf(f59,axiom,
( frontsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
fof(f59_nnf,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f59]) ).
fof(f59_sk,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f59_nnf]) ).
cnf(c59,plain,
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(t84,plain,
ifeq(ssList(X1),true,frontsegP(X1,nil),true) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(t530,plain,
ifeq(ssList(X1),true,frontsegP(X1,nil),true) = true,
inference(orient,[status(thm)],[t84]) ).
cnf(t9620,plain,
ifeq(ssList(X1),true,frontsegP(X1,sk2),true) = true,
inference(step,[status(thm)],[t530,t577]) ).
cnf(t581,plain,
ifeq(ssList(X1),true,frontsegP(X1,sk2),true) = true,
inference(rw,[status(thm)],[t9620]) ).
cnf(t10342,plain,
ifeq(ssList(X1),true,frontsegP(X1,sk4),true) = true,
inference(step,[status(thm)],[t581,t672]) ).
cnf(t9491,plain,
ifeq(ssList(X1),true,frontsegP(X1,sk4),true) = true,
inference(orient,[status(thm)],[t10342]) ).
cnf(t9519,plain,
true = ifeq(true,true,frontsegP(sk3,sk4),true),
inference(cp,[status(thm)],[t9491,t2497]) ).
cnf(t10345,plain,
true = frontsegP(sk3,sk4),
inference(step,[status(thm)],[t9519,t221]) ).
cnf(t9528,plain,
frontsegP(sk3,sk4) = true,
inference(orient,[status(thm)],[t10345]) ).
cnf(t9531,plain,
sk3 = ifeq(true,true,ifeq(frontsegP(sk4,sk3),true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,sk4,sk3),sk3),sk3),sk3),
inference(cp,[status(thm)],[t236,t9528]) ).
cnf(t10350,plain,
sk3 = ifeq(frontsegP(sk4,sk3),true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,sk4,sk3),sk3),sk3),
inference(step,[status(thm)],[t9531,t221]) ).
cnf(f196,negated_conjecture,
( frontsegP(sk4,sk3)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(t75,plain,
or(eq(nil,sk3),frontsegP(sk4,sk3)) = true,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t9677,plain,
or(eq(sk2,sk3),frontsegP(sk4,sk3)) = true,
inference(step,[status(thm)],[t75,t577]) ).
cnf(t633,plain,
or(eq(sk2,sk3),frontsegP(sk4,sk3)) = true,
inference(orient,[status(thm)],[t9677]) ).
cnf(t9693,plain,
or(eq(sk4,sk3),frontsegP(sk4,sk3)) = true,
inference(step,[status(thm)],[t633,t672]) ).
cnf(t678,plain,
or(eq(sk4,sk3),frontsegP(sk4,sk3)) = true,
inference(rw,[status(thm)],[t9693]) ).
cnf(t9935,plain,
or(false,frontsegP(sk4,sk3)) = true,
inference(step,[status(thm)],[t678,t6547]) ).
cnf(t9936,plain,
frontsegP(sk4,sk3) = true,
inference(step,[status(thm)],[t9935,t264]) ).
cnf(t8048,plain,
frontsegP(sk4,sk3) = true,
inference(orient,[status(thm)],[t9936]) ).
cnf(t10351,plain,
sk3 = ifeq(true,true,ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,sk4,sk3),sk3),sk3),
inference(step,[status(thm)],[t10350,t8048]) ).
cnf(t10352,plain,
sk3 = ifeq(ssList(sk3),true,ifeq(ssList(sk4),true,sk4,sk3),sk3),
inference(step,[status(thm)],[t10351,t221]) ).
cnf(t10353,plain,
sk3 = ifeq(true,true,ifeq(ssList(sk4),true,sk4,sk3),sk3),
inference(step,[status(thm)],[t10352,t2497]) ).
cnf(t10354,plain,
sk3 = ifeq(ssList(sk4),true,sk4,sk3),
inference(step,[status(thm)],[t10353,t221]) ).
cnf(t10355,plain,
sk3 = ifeq(true,true,sk4,sk3),
inference(step,[status(thm)],[t10354,t2356]) ).
cnf(t10356,plain,
sk3 = sk4,
inference(step,[status(thm)],[t10355,t221]) ).
cnf(t9541,plain,
sk3 = sk4,
inference(orient,[status(thm)],[t10356]) ).
cnf(t10360,plain,
ifeq(sk4,sk4,false,true) = true,
inference(step,[status(thm)],[t8046,t9541]) ).
cnf(t10361,plain,
false = true,
inference(step,[status(thm)],[t10360,t221]) ).
cnf(t9545,plain,
false = true,
inference(rw,[status(thm)],[t10361]) ).
cnf(t9555,plain,
false = true,
inference(orient,[status(thm)],[t9545]) ).
cnf(f10,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
fof(f10_nnf,plain,
~ singletonP(nil),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ singletonP(nil),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f53,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
fof(f53_nnf,plain,
skac3 != skac2,
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
skac3 != skac2,
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
skac3 != skac2,
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(f62,axiom,
( ~ ssItem(U)
| ~ lt(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
fof(f62_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(f70,axiom,
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f70_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f97,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f97_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(nnf_transformation,[status(thm)],[f97]) ).
fof(f97_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(skolemisation,[status(esa)],[f97_nnf]) ).
cnf(c97,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(esa)],[f97_sk]) ).
cnf(f98,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
fof(f98_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c98,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(f109,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
fof(f109_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(f110,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
fof(f110_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f110]) ).
fof(f110_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f110_nnf]) ).
cnf(c110,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f110_sk]) ).
cnf(f113,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
fof(f113_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(f116,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
fof(f116_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f178,axiom,
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).
fof(f178_nnf,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(nnf_transformation,[status(thm)],[f178]) ).
fof(f178_sk,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(skolemisation,[status(esa)],[f178_nnf]) ).
cnf(c178,plain,
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(f184,axiom,
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).
fof(f184_nnf,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(nnf_transformation,[status(thm)],[f184]) ).
fof(f184_sk,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(skolemisation,[status(esa)],[f184_nnf]) ).
cnf(c184,plain,
( ~ ssList(X5)
| ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f184_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c53,c62,c70,c97,c98,c109,c110,c113,c114,c116,c178,c184,c192]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t9555]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC038-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 16:02:44 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 21.24/3.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.24/3.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------