%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN224-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 03:34:07 PM UTC 2026
% Result : Unsatisfiable 6.39s 1.28s
% Output : Proof 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 36 unt; 0 def)
% Number of atoms : 80 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 34 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 39 ( 8 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f368,negated_conjecture,
~ l3(a,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
! [X] : ~ l3(a,X),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
! [X] : ~ l3(a,X),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ l3(a,X0),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(t118,plain,
eq(l3(a,X1),true) = efalse,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(t417,plain,
eq(l3(a,X1),true) = efalse,
inference(orient,[status(thm)],[t118]) ).
cnf(f143,axiom,
( ~ s0(B)
| q1(B,B,B) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f161,axiom,
( ~ q1(d,E,d)
| ~ s0(d)
| ~ q0(D,E)
| r1(D) ),
file('/export/starexec/sandbox2/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/sandbox2/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(h184,plain,
r1(V0) = true,
inference(hyper_resolution,[status(thm)],[hi159,hi16,hi0,h0]) ).
cnf(f225,axiom,
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_188) ).
fof(f225_nnf,plain,
! [G] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(nnf_transformation,[status(thm)],[f225]) ).
fof(f225_sk,plain,
! [G] :
( ~ l0(G)
| ~ r1(G)
| r2(G) ),
inference(skolemisation,[status(esa)],[f225_nnf]) ).
cnf(c225,plain,
( ~ l0(X0)
| ~ r1(X0)
| r2(X0) ),
inference(cnf_transformation,[status(esa)],[f225_sk]) ).
cnf(hi222,axiom,
ifeq(r1(X0),true,ifeq(l0(X0),true,r2(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c225]) ).
cnf(f19,axiom,
l0(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
fof(f19_nnf,plain,
l0(a),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
l0(a),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
l0(a) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h187,plain,
r2(a) = true,
inference(hyper_resolution,[status(thm)],[hi222,h184,hi19]) ).
cnf(f255,axiom,
( ~ r2(B)
| l3(B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_218) ).
fof(f255_nnf,plain,
! [B] :
( ~ r2(B)
| l3(B,B) ),
inference(nnf_transformation,[status(thm)],[f255]) ).
fof(f255_sk,plain,
! [B] :
( ~ r2(B)
| l3(B,B) ),
inference(skolemisation,[status(esa)],[f255_nnf]) ).
cnf(c255,plain,
( ~ r2(X0)
| l3(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f255_sk]) ).
cnf(hi250,axiom,
ifeq(r2(X0),true,l3(X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c255]) ).
cnf(t36,plain,
l3(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi250,h187]) ).
cnf(t346,plain,
l3(a,a) = true,
inference(orient,[status(thm)],[t36]) ).
cnf(t418,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t417,t346]) ).
cnf(t13,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t416,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t13]) ).
cnf(t454,plain,
efalse = etrue,
inference(step,[status(thm)],[t418,t416]) ).
cnf(t419,plain,
efalse = etrue,
inference(orient,[status(thm)],[t454]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t419]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN224-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 00:33:18 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.39/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.39/1.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------