%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN113-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 9.17s 1.72s
% Output : Proof 9.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 31 unt; 0 def)
% Number of atoms : 79 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 34 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 68 ( 17 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f143,axiom,
( ~ s0(B)
| q1(B,B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_106) ).
fof(f143_nnf,plain,
! [B] :
( ~ s0(B)
| q1(B,B,B) ),
inference(nnf_transformation,[status(thm)],[f143]) ).
fof(f143_sk,plain,
! [B] :
( ~ s0(B)
| q1(B,B,B) ),
inference(skolemisation,[status(esa)],[f143_nnf]) ).
cnf(c143,plain,
( ~ s0(X0)
| q1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(hi141,axiom,
ifeq(s0(X0),true,q1(X0,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c143]) ).
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(h0,plain,
q1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi141,hi0]) ).
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(h120,plain,
k2(d,d) = true,
inference(hyper_resolution,[status(thm)],[hi164,h0]) ).
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(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(h98,plain,
k1(d) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi33]) ).
cnf(f42,axiom,
( ~ m0(C,C,B)
| m1(B,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_005) ).
fof(f42_nnf,plain,
! [B,C] :
( ~ m0(C,C,B)
| m1(B,C,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [B,C] :
( ~ m0(C,C,B)
| m1(B,C,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( ~ m0(X1,X1,X0)
| m1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(m0(X0,X0,X1),true,m1(X1,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
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(h59,plain,
m1(V0,d,V0) = true,
inference(hyper_resolution,[status(thm)],[hi42,hi18]) ).
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(t6,plain,
k2(X1,d) = true,
inference(hyper_resolution,[status(thm)],[hi162,h59,h98,h120]) ).
cnf(t657,plain,
k2(X1,d) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f368,negated_conjecture,
~ k2(e,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ k2(e,d),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ k2(e,d),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ k2(e,d),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
k2(e,d) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t657]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN113-1 : 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 : n017.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 00:08:31 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.17/1.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.17/1.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------