%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN167-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 03:33:58 PM UTC 2026
% Result : Unsatisfiable 2.44s 0.77s
% Output : Proof 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 29 unt; 0 def)
% Number of atoms : 53 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 62 ( 25 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f119,axiom,
( ~ p1(J,H,A)
| ~ m0(J,H,A)
| p1(H,I,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_082) ).
fof(f119_nnf,plain,
! [H,I,J,A] :
( ~ p1(J,H,A)
| ~ m0(J,H,A)
| p1(H,I,J) ),
inference(nnf_transformation,[status(thm)],[f119]) ).
fof(f119_sk,plain,
! [H,I,J,A] :
( ~ p1(J,H,A)
| ~ m0(J,H,A)
| p1(H,I,J) ),
inference(skolemisation,[status(esa)],[f119_nnf]) ).
cnf(c119,plain,
( ~ p1(X2,X0,X3)
| ~ m0(X2,X0,X3)
| p1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f119_sk]) ).
cnf(t21,plain,
ifeq(m0(X1,X2,X3),true,ifeq(p1(X1,X2,X3),true,p1(X2,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(t28,plain,
ifeq(m0(X1,X2,X3),true,ifeq(p1(X1,X2,X3),true,p1(X2,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f109,axiom,
( ~ s0(F)
| ~ s0(G)
| p1(F,F,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_072) ).
fof(f109_nnf,plain,
! [F,G] :
( ~ s0(F)
| ~ s0(G)
| p1(F,F,F) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [F,G] :
( ~ s0(F)
| ~ s0(G)
| p1(F,F,F) ),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
( ~ s0(X0)
| ~ s0(X1)
| p1(X0,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(hi108,axiom,
ifeq(s0(X0),true,ifeq(s0(X1),true,p1(X1,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
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(t5,plain,
p1(d,d,d) = true,
inference(hyper_resolution,[status(thm)],[hi108,hi0,hi0]) ).
cnf(t69,plain,
p1(d,d,d) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t70,plain,
true = ifeq(m0(d,d,d),true,ifeq(true,true,p1(d,X1,d),true),true),
inference(cp,[status(thm)],[t28,t69]) ).
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(t0,plain,
m0(X1,d,X2) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t44,plain,
m0(X1,d,X2) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t120,plain,
true = ifeq(true,true,ifeq(true,true,p1(d,X1,d),true),true),
inference(step,[status(thm)],[t70,t44]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t121,plain,
true = ifeq(true,true,p1(d,X1,d),true),
inference(step,[status(thm)],[t120,t27]) ).
cnf(t122,plain,
true = p1(d,X1,d),
inference(step,[status(thm)],[t121,t27]) ).
cnf(t102,plain,
p1(d,X1,d) = true,
inference(orient,[status(thm)],[t122]) ).
cnf(f368,negated_conjecture,
~ p1(d,X,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
! [X] : ~ p1(d,X,d),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
! [X] : ~ p1(d,X,d),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ p1(d,X0,d),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
p1(d,X1,d) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t102]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN167-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 25 00:21:50 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.44/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.44/0.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------