%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 03:32:07 PM UTC 2026
% Result : Theorem 20.50s 3.41s
% Output : Proof 20.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 20
% Syntax : Number of formulae : 120 ( 115 unt; 0 def)
% Number of atoms : 125 ( 124 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 61 ( 56 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 125 ( 15 sgn 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
pB != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(f15_nnf,plain,
pB != pE,
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
pB != pE,
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
pB != pE,
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t14,plain,
ifeq(pB,pE,false,true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t47,plain,
ifeq(pB,pE,false,true) = true,
inference(orient,[status(thm)],[t14]) ).
fof(f17,axiom,
! [X,X2] : proj2C(c2(X,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
fof(f17_nnf,plain,
! [X,X2] : proj2C(c2(X,X2)) = X2,
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,X2] : proj2C(c2(X,X2)) = X2,
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
proj2C(c2(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t8,plain,
proj2C(c2(X1,X2)) = X2,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t34,plain,
proj2C(c2(X1,X2)) = X2,
inference(orient,[status(thm)],[t8]) ).
fof(f26,conjecture,
? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_027) ).
fof(f26_neg,negated_conjecture,
~ ? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
! [U,V] :
( U = V
| linC(U) != linC(V) ),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
! [U,V] :
( U = V
| linC(U) != linC(V) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( X0 = X1
| linC(X0) != linC(X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t22,plain,
ifeq(linC(X1),linC(X2),X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t29,plain,
ifeq(linC(X1),linC(X2),X1,X2) = X2,
inference(orient,[status(thm)],[t22]) ).
fof(f25,axiom,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(f25_nnf,plain,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
linC(c2(X0,X1)) = append(linP(X0),linP(X1)),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t24,plain,
append(linP(X1),linP(X2)) = linC(c2(X1,X2)),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t73,plain,
append(linP(X1),linP(X2)) = linC(c2(X1,X2)),
inference(orient,[status(thm)],[t24]) ).
fof(f24,axiom,
linP(pE) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(f24_nnf,plain,
linP(pE) = nil,
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
linP(pE) = nil,
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(t0,plain,
linP(pE) = nil,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t60,plain,
linP(pE) = nil,
inference(orient,[status(thm)],[t0]) ).
cnf(t75,plain,
linC(c2(X1,pE)) = append(linP(X1),nil),
inference(cp,[status(thm)],[t73,t60]) ).
cnf(t89,plain,
linC(c2(X1,pE)) = append(linP(X1),nil),
inference(orient,[status(thm)],[t75]) ).
cnf(t90,plain,
X1 = ifeq(append(linP(X2),nil),linC(X1),c2(X2,pE),X1),
inference(cp,[status(thm)],[t29,t89]) ).
cnf(t511,plain,
ifeq(append(linP(X1),nil),linC(X2),c2(X1,pE),X2) = X2,
inference(orient,[status(thm)],[t90]) ).
fof(f19,axiom,
! [Y,Z,Xs] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(f19_nnf,plain,
! [Y,Z,Xs] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Z,Xs,Y] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
append(cons(X1,X2),X0) = cons(X1,append(X2,X0)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t25,plain,
cons(X1,append(X2,X3)) = append(cons(X1,X2),X3),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t49,plain,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
inference(orient,[status(thm)],[t25]) ).
fof(f23,axiom,
linP(pB) = cons(b,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(f23_nnf,plain,
linP(pB) = cons(b,nil),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
linP(pB) = cons(b,nil),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(t5,plain,
cons(b,nil) = linP(pB),
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t55,plain,
cons(b,nil) = linP(pB),
inference(orient,[status(thm)],[t5]) ).
cnf(t56,plain,
cons(b,append(nil,X1)) = append(linP(pB),X1),
inference(cp,[status(thm)],[t49,t55]) ).
fof(f18,axiom,
! [Y] : append(nil,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(f18_nnf,plain,
! [Y] : append(nil,Y) = Y,
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Y] : append(nil,Y) = Y,
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
append(nil,X0) = X0,
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t1,plain,
append(nil,X1) = X1,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t30,plain,
append(nil,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t7691,plain,
cons(b,X1) = append(linP(pB),X1),
inference(step,[status(thm)],[t56,t30]) ).
cnf(t87,plain,
append(linP(pB),X1) = cons(b,X1),
inference(orient,[status(thm)],[t7691]) ).
cnf(t518,plain,
X1 = ifeq(cons(b,nil),linC(X1),c2(pB,pE),X1),
inference(cp,[status(thm)],[t511,t87]) ).
cnf(t7756,plain,
X1 = ifeq(linP(pB),linC(X1),c2(pB,pE),X1),
inference(step,[status(thm)],[t518,t55]) ).
cnf(t543,plain,
ifeq(linP(pB),linC(X1),c2(pB,pE),X1) = X1,
inference(orient,[status(thm)],[t7756]) ).
cnf(t74,plain,
linC(c2(pE,X1)) = append(nil,linP(X1)),
inference(cp,[status(thm)],[t73,t60]) ).
cnf(t7689,plain,
linC(c2(pE,X1)) = linP(X1),
inference(step,[status(thm)],[t74,t30]) ).
cnf(t82,plain,
linC(c2(pE,X1)) = linP(X1),
inference(orient,[status(thm)],[t7689]) ).
cnf(t557,plain,
c2(pE,X1) = ifeq(linP(pB),linP(X1),c2(pB,pE),c2(pE,X1)),
inference(cp,[status(thm)],[t543,t82]) ).
cnf(t7309,plain,
ifeq(linP(pB),linP(X1),c2(pB,pE),c2(pE,X1)) = c2(pE,X1),
inference(orient,[status(thm)],[t557]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t7310,plain,
c2(pE,pB) = c2(pB,pE),
inference(cp,[status(thm)],[t7309,t28]) ).
cnf(t7312,plain,
c2(pB,pE) = c2(pE,pB),
inference(orient,[status(thm)],[t7310]) ).
cnf(t7313,plain,
pE = proj2C(c2(pE,pB)),
inference(cp,[status(thm)],[t34,t7312]) ).
cnf(t8428,plain,
pE = pB,
inference(step,[status(thm)],[t7313,t34]) ).
cnf(t7315,plain,
pB = pE,
inference(orient,[status(thm)],[t8428]) ).
cnf(t8683,plain,
ifeq(pE,pE,false,true) = true,
inference(step,[status(thm)],[t47,t7315]) ).
cnf(t8684,plain,
false = true,
inference(step,[status(thm)],[t8683,t28]) ).
cnf(t7508,plain,
false = true,
inference(rw,[status(thm)],[t8684]) ).
cnf(t7653,plain,
false = true,
inference(orient,[status(thm)],[t7508]) ).
fof(f2,axiom,
! [X,X2] : nil != cons(X,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
fof(f2_nnf,plain,
! [X,X2] : nil != cons(X,X2),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,X2] : nil != cons(X,X2),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
nil != cons(X0,X1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f3,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(f3_nnf,plain,
a != b,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
a != b,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
a != b,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f6,axiom,
! [X,X2] : aP(X) != bP(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(f6_nnf,plain,
! [X,X2] : aP(X) != bP(X2),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,X2] : aP(X) != bP(X2),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
aP(X0) != bP(X1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f7,axiom,
! [X] : aP(X) != pA,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(f7_nnf,plain,
! [X] : aP(X) != pA,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] : aP(X) != pA,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
aP(X0) != pA,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f8,axiom,
! [X] : aP(X) != pB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(f8_nnf,plain,
! [X] : aP(X) != pB,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : aP(X) != pB,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
aP(X0) != pB,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f9,axiom,
! [X] : aP(X) != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f9_nnf,plain,
! [X] : aP(X) != pE,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : aP(X) != pE,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
aP(X0) != pE,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f10,axiom,
! [X] : bP(X) != pA,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f10_nnf,plain,
! [X] : bP(X) != pA,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : bP(X) != pA,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
bP(X0) != pA,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f11,axiom,
! [X] : bP(X) != pB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f11_nnf,plain,
! [X] : bP(X) != pB,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : bP(X) != pB,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
bP(X0) != pB,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f12,axiom,
! [X] : bP(X) != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(f12_nnf,plain,
! [X] : bP(X) != pE,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] : bP(X) != pE,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
bP(X0) != pE,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f13,axiom,
pA != pB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(f13_nnf,plain,
pA != pB,
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
pA != pB,
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
pA != pB,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f14,axiom,
pA != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(f14_nnf,plain,
pA != pE,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
pA != pE,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
pA != pE,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c3,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t7653]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 23:43:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.50/3.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.50/3.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------