%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC328-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 03:06:01 PM UTC 2026
% Result : Unsatisfiable 19.41s 3.31s
% Output : Proof 19.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 24
% Syntax : Number of formulae : 120 ( 68 unt; 0 def)
% Number of atoms : 272 ( 85 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 362 ( 210 ~; 152 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 127 ( 2 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f55,axiom,
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
fof(f55_nnf,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(t82,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t542,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(orient,[status(thm)],[t82]) ).
cnf(f189,negated_conjecture,
nil = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f189_nnf,plain,
nil = sk3,
inference(nnf_transformation,[status(thm)],[f189]) ).
cnf(c189,plain,
nil = sk3,
inference(cnf_transformation,[status(esa)],[f189_nnf]) ).
cnf(t0,plain,
sk3 = nil,
inference(equality_encoding,[status(esa)],[c189]) ).
cnf(t587,plain,
nil = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t9222,plain,
ifeq(ssList(X1),true,segmentP(X1,sk3),true) = true,
inference(step,[status(thm)],[t542,t587]) ).
cnf(t589,plain,
ifeq(ssList(X1),true,segmentP(X1,sk3),true) = true,
inference(rw,[status(thm)],[t9222]) ).
cnf(t9122,plain,
ifeq(ssList(X1),true,segmentP(X1,sk3),true) = true,
inference(orient,[status(thm)],[t589]) ).
cnf(f186,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
fof(f186_nnf,plain,
ssList(sk2),
inference(nnf_transformation,[status(thm)],[f186]) ).
cnf(c186,plain,
ssList(sk2),
inference(cnf_transformation,[status(esa)],[f186_nnf]) ).
cnf(t13,plain,
ssList(sk2) = true,
inference(equality_encoding,[status(esa)],[c186]) ).
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(t670,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t2]) ).
cnf(t9294,plain,
ssList(sk4) = true,
inference(step,[status(thm)],[t13,t670]) ).
cnf(t2475,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t9294]) ).
cnf(t9150,plain,
true = ifeq(true,true,segmentP(sk4,sk3),true),
inference(cp,[status(thm)],[t9122,t2475]) ).
cnf(t68,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t217,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t68]) ).
cnf(t9847,plain,
true = segmentP(sk4,sk3),
inference(step,[status(thm)],[t9150,t217]) ).
cnf(t70,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t330,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t70]) ).
cnf(f192,negated_conjecture,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(nnf_transformation,[status(thm)],[f192]) ).
fof(f192_sk,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(skolemisation,[status(esa)],[f192_nnf]) ).
cnf(c192,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(cnf_transformation,[status(esa)],[f192_sk]) ).
cnf(t85,plain,
or(not(segmentP(sk2,sk1)),not(equalelemsP(sk1))) = true,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t584,plain,
or(not(segmentP(sk2,sk1)),not(equalelemsP(sk1))) = true,
inference(orient,[status(thm)],[t85]) ).
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(t662,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t1]) ).
cnf(t9283,plain,
or(not(segmentP(sk2,sk3)),not(equalelemsP(sk1))) = true,
inference(step,[status(thm)],[t584,t662]) ).
cnf(t9284,plain,
or(not(segmentP(sk2,sk3)),not(equalelemsP(sk3))) = true,
inference(step,[status(thm)],[t9283,t662]) ).
cnf(f0,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
fof(f0_nnf,plain,
equalelemsP(nil),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
equalelemsP(nil),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t5,plain,
equalelemsP(nil) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t9281,plain,
equalelemsP(sk3) = true,
inference(step,[status(thm)],[t5,t587]) ).
cnf(t652,plain,
equalelemsP(sk3) = true,
inference(orient,[status(thm)],[t9281]) ).
cnf(t9285,plain,
or(not(segmentP(sk2,sk3)),not(true)) = true,
inference(step,[status(thm)],[t9284,t652]) ).
cnf(t7,plain,
not(true) = false,
introduced(definition) ).
cnf(t633,plain,
not(true) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t9286,plain,
or(not(segmentP(sk2,sk3)),false) = true,
inference(step,[status(thm)],[t9285,t633]) ).
cnf(t22,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t259,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t22]) ).
cnf(t9287,plain,
not(segmentP(sk2,sk3)) = true,
inference(step,[status(thm)],[t9286,t259]) ).
cnf(t663,plain,
not(segmentP(sk2,sk3)) = true,
inference(rw,[status(thm)],[t9287]) ).
cnf(t9309,plain,
not(segmentP(sk4,sk3)) = true,
inference(step,[status(thm)],[t663,t670]) ).
cnf(t6603,plain,
not(segmentP(sk4,sk3)) = true,
inference(orient,[status(thm)],[t9309]) ).
cnf(t6604,plain,
false = ifeq(true,true,segmentP(sk4,sk3),false),
inference(cp,[status(thm)],[t330,t6603]) ).
cnf(t9310,plain,
false = segmentP(sk4,sk3),
inference(step,[status(thm)],[t6604,t217]) ).
cnf(t6605,plain,
segmentP(sk4,sk3) = false,
inference(orient,[status(thm)],[t9310]) ).
cnf(t9848,plain,
true = false,
inference(step,[status(thm)],[t9847,t6605]) ).
cnf(t9159,plain,
false = true,
inference(orient,[status(thm)],[t9848]) ).
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(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(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,t9159]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC328-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 17:39:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 19.41/3.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.41/3.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------