%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN109-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 03:33:50 PM UTC 2026
% Result : Unsatisfiable 6.07s 1.31s
% Output : Proof 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 34 unt; 0 def)
% Number of atoms : 86 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 9 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f132,axiom,
( ~ p0(G,F)
| q1(F,G,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_095) ).
fof(f132_nnf,plain,
! [F,G] :
( ~ p0(G,F)
| q1(F,G,G) ),
inference(nnf_transformation,[status(thm)],[f132]) ).
fof(f132_sk,plain,
! [F,G] :
( ~ p0(G,F)
| q1(F,G,G) ),
inference(skolemisation,[status(esa)],[f132_nnf]) ).
cnf(c132,plain,
( ~ p0(X1,X0)
| q1(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f132_sk]) ).
cnf(hi130,axiom,
ifeq(p0(X0,X1),true,q1(X1,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c132]) ).
cnf(f17,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
fof(f17_nnf,plain,
p0(c,b),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
p0(c,b),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
p0(c,b) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h45,plain,
q1(b,c,c) = true,
inference(hyper_resolution,[status(thm)],[hi130,hi17]) ).
cnf(f166,axiom,
( ~ q1(A,J,J)
| k2(J,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_129) ).
fof(f166_nnf,plain,
! [J,A] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(nnf_transformation,[status(thm)],[f166]) ).
fof(f166_sk,plain,
! [J,A] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemisation,[status(esa)],[f166_nnf]) ).
cnf(c166,plain,
( ~ q1(X1,X0,X0)
| k2(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f166_sk]) ).
cnf(hi164,axiom,
ifeq(q1(X0,X1,X1),true,k2(X1,X1),true) = true,
inference(equality_encoding,[status(esa)],[c166]) ).
cnf(h202,plain,
k2(c,c) = true,
inference(hyper_resolution,[status(thm)],[hi164,h45]) ).
cnf(f38,axiom,
( ~ n0(J,I)
| k1(I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).
fof(f38_nnf,plain,
! [I,J] :
( ~ n0(J,I)
| k1(I) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [I,J] :
( ~ n0(J,I)
| k1(I) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( ~ n0(X1,X0)
| k1(X0) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi38,axiom,
ifeq(n0(X0,X1),true,k1(X1),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(f25,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
fof(f25_nnf,plain,
n0(d,c),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
n0(d,c),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,axiom,
n0(d,c) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h85,plain,
k1(c) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi25]) ).
cnf(f72,axiom,
( ~ l0(J)
| ~ r0(I)
| m1(I,J,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_035) ).
fof(f72_nnf,plain,
! [I,J] :
( ~ l0(J)
| ~ r0(I)
| m1(I,J,I) ),
inference(nnf_transformation,[status(thm)],[f72]) ).
fof(f72_sk,plain,
! [I,J] :
( ~ l0(J)
| ~ r0(I)
| m1(I,J,I) ),
inference(skolemisation,[status(esa)],[f72_nnf]) ).
cnf(c72,plain,
( ~ l0(X1)
| ~ r0(X0)
| m1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f72_sk]) ).
cnf(hi72,axiom,
ifeq(r0(X0),true,ifeq(l0(X1),true,m1(X0,X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(f8,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f8_nnf,plain,
r0(b),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
r0(b),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi8,axiom,
r0(b) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f23,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
fof(f23_nnf,plain,
l0(c),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
l0(c),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,axiom,
l0(c) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h69,plain,
m1(b,c,b) = true,
inference(hyper_resolution,[status(thm)],[hi72,hi8,hi23]) ).
cnf(f164,axiom,
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_127) ).
fof(f164_nnf,plain,
! [C,D,E,F] :
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(nnf_transformation,[status(thm)],[f164]) ).
fof(f164_sk,plain,
! [C,D,E,F] :
( ~ k2(F,D)
| ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(skolemisation,[status(esa)],[f164_nnf]) ).
cnf(c164,plain,
( ~ k2(X3,X1)
| ~ k1(X3)
| ~ m1(X2,X1,X0)
| k2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f164_sk]) ).
cnf(hi162,axiom,
ifeq(m1(X0,X1,X2),true,ifeq(k1(X3),true,ifeq(k2(X3,X1),true,k2(X2,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c164]) ).
cnf(t7,plain,
k2(b,c) = true,
inference(hyper_resolution,[status(thm)],[hi162,h69,h85,h202]) ).
cnf(t424,plain,
k2(b,c) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f368,negated_conjecture,
~ k2(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ k2(b,c),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ k2(b,c),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ k2(b,c),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
k2(b,c) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t424]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN109-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 00:14:49 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.07/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.07/1.31 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------