%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN178-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 03:34:00 PM UTC 2026
% Result : Unsatisfiable 7.71s 1.43s
% Output : Proof 7.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 51 unt; 0 def)
% Number of atoms : 127 ( 22 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 110 ( 58 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 105 ( 28 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f122,axiom,
( ~ p0(C,B)
| p1(B,B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).
fof(f122_nnf,plain,
! [B,C] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [B,C] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( ~ p0(X1,X0)
| p1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(hi120,axiom,
ifeq(p0(X0,X1),true,p1(X1,X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(f13,axiom,
p0(b,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f13_nnf,plain,
! [X] : p0(b,X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : p0(b,X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
p0(b,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
p0(b,X0) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h41,plain,
p1(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi120,hi13]) ).
cnf(f218,axiom,
( ~ p1(I,I,I)
| q2(I,I,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_181) ).
fof(f218_nnf,plain,
! [I] :
( ~ p1(I,I,I)
| q2(I,I,I) ),
inference(nnf_transformation,[status(thm)],[f218]) ).
fof(f218_sk,plain,
! [I] :
( ~ p1(I,I,I)
| q2(I,I,I) ),
inference(skolemisation,[status(esa)],[f218_nnf]) ).
cnf(c218,plain,
( ~ p1(X0,X0,X0)
| q2(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f218_sk]) ).
cnf(hi215,axiom,
ifeq(p1(X0,X0,X0),true,q2(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c218]) ).
cnf(h187,plain,
q2(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi215,h41]) ).
cnf(f129,axiom,
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_092) ).
fof(f129_nnf,plain,
! [J,A,B,C] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(nnf_transformation,[status(thm)],[f129]) ).
fof(f129_sk,plain,
! [J,A,B,C] :
( ~ p0(C,J)
| ~ n0(B,A)
| q1(J,A,J) ),
inference(skolemisation,[status(esa)],[f129_nnf]) ).
cnf(c129,plain,
( ~ p0(X3,X0)
| ~ n0(X2,X1)
| q1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f129_sk]) ).
cnf(hi127,axiom,
ifeq(n0(X0,X1),true,ifeq(p0(X2,X3),true,q1(X3,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c129]) ).
cnf(f33,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
fof(f33_nnf,plain,
n0(c,d),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
n0(c,d),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi33,axiom,
n0(c,d) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(h71,plain,
q1(V0,d,V0) = true,
inference(hyper_resolution,[status(thm)],[hi127,hi33,hi13]) ).
cnf(f161,axiom,
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_124) ).
fof(f161_nnf,plain,
! [D,E] :
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
inference(nnf_transformation,[status(thm)],[f161]) ).
fof(f161_sk,plain,
! [D,E] :
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
inference(skolemisation,[status(esa)],[f161_nnf]) ).
cnf(c161,plain,
( ~ q1(d,X1,d)
| ~ s0(d)
| ~ q0(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f161_sk]) ).
cnf(hi159,axiom,
ifeq(q0(X0,X1),true,ifeq(s0(d),true,ifeq(q1(d,X1,d),true,r1(X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c161]) ).
cnf(f16,axiom,
q0(X,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
fof(f16_nnf,plain,
! [X] : q0(X,d),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : q0(X,d),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
q0(X0,d),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
q0(X0,d) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f0,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
s0(d),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
s0(d),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,axiom,
s0(d) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h215,plain,
r1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi159,hi16,hi0,h71]) ).
cnf(f224,axiom,
( ~ q2(D,D,D)
| ~ k0(D)
| ~ m0(E,F,C)
| ~ r1(D)
| q2(C,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_187) ).
fof(f224_nnf,plain,
! [C,D,E,F] :
( ~ q2(D,D,D)
| ~ k0(D)
| ~ m0(E,F,C)
| ~ r1(D)
| q2(C,D,C) ),
inference(nnf_transformation,[status(thm)],[f224]) ).
fof(f224_sk,plain,
! [C,D,E,F] :
( ~ q2(D,D,D)
| ~ k0(D)
| ~ m0(E,F,C)
| ~ r1(D)
| q2(C,D,C) ),
inference(skolemisation,[status(esa)],[f224_nnf]) ).
cnf(c224,plain,
( ~ q2(X1,X1,X1)
| ~ k0(X1)
| ~ m0(X2,X3,X0)
| ~ r1(X1)
| q2(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f224_sk]) ).
cnf(hi221,axiom,
ifeq(r1(X0),true,ifeq(m0(X1,X2,X3),true,ifeq(k0(X0),true,ifeq(q2(X0,X0,X0),true,q2(X3,X0,X3),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c224]) ).
cnf(f18,axiom,
m0(X,d,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
fof(f18_nnf,plain,
! [X,Y] : m0(X,d,Y),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] : m0(X,d,Y),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
m0(X0,d,X1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
m0(X0,d,X1) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f31,axiom,
k0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
fof(f31_nnf,plain,
k0(b),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
k0(b),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi31,axiom,
k0(b) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h387,plain,
q2(V0,b,V0) = true,
inference(hyper_resolution,[status(thm)],[hi221,h215,hi18,hi31,h187]) ).
cnf(f292,axiom,
( ~ n0(I,G)
| ~ q2(I,G,H)
| q3(G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_255) ).
fof(f292_nnf,plain,
! [G,H,I] :
( ~ n0(I,G)
| ~ q2(I,G,H)
| q3(G,H) ),
inference(nnf_transformation,[status(thm)],[f292]) ).
fof(f292_sk,plain,
! [G,H,I] :
( ~ n0(I,G)
| ~ q2(I,G,H)
| q3(G,H) ),
inference(skolemisation,[status(esa)],[f292_nnf]) ).
cnf(c292,plain,
( ~ n0(X2,X0)
| ~ q2(X2,X0,X1)
| q3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f292_sk]) ).
cnf(hi287,axiom,
ifeq(q2(X0,X1,X2),true,ifeq(n0(X0,X1),true,q3(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c292]) ).
cnf(f6,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f6_nnf,plain,
n0(d,b),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
n0(d,b),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi6,axiom,
n0(d,b) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t32,plain,
q3(b,d) = true,
inference(hyper_resolution,[status(thm)],[hi287,h387,hi6]) ).
cnf(t175,plain,
q3(b,d) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(f368,negated_conjecture,
~ q3(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ q3(b,d),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ q3(b,d),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ q3(b,d),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
q3(b,d) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t175]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN178-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 00:30:08 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.71/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.71/1.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------