%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN685-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 03:35:29 PM UTC 2026
% Result : Unsatisfiable 26.28s 3.77s
% Output : Proof 26.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 58 unt; 0 def)
% Number of atoms : 82 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 51 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,negated_conjecture,
( ~ p2(X28,X30)
| ~ p2(X28,X29)
| p2(X29,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_31) ).
fof(f30_nnf,plain,
! [X29,X30,X28] :
( ~ p2(X28,X30)
| ~ p2(X28,X29)
| p2(X29,X30) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X29,X30,X28] :
( ~ p2(X28,X30)
| ~ p2(X28,X29)
| p2(X29,X30) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t40,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t67,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(f39,negated_conjecture,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_40) ).
fof(f39_nnf,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(nnf_transformation,[status(thm)],[f39]) ).
cnf(c39,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(cnf_transformation,[status(esa)],[f39_nnf]) ).
cnf(t32,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t115,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t117,plain,
true = ifeq(p2(f11(f4(c32),c34),X1),true,ifeq(true,true,p2(X1,f18(f11(f4(c36),c34),f9(f17(c31)))),true),true),
inference(cp,[status(thm)],[t67,t115]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t62,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t12086,plain,
true = ifeq(p2(f11(f4(c32),c34),X1),true,p2(X1,f18(f11(f4(c36),c34),f9(f17(c31)))),true),
inference(step,[status(thm)],[t117,t62]) ).
cnf(t11479,plain,
ifeq(p2(f11(f4(c32),c34),X1),true,p2(X1,f18(f11(f4(c36),c34),f9(f17(c31)))),true) = true,
inference(orient,[status(thm)],[t12086]) ).
cnf(f6,negated_conjecture,
p2(X28,X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_7) ).
fof(f6_nnf,plain,
! [X28] : p2(X28,X28),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X28] : p2(X28,X28),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t9,plain,
p2(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t98,plain,
p2(X1,X1) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t100,plain,
true = ifeq(p2(X1,X2),true,ifeq(true,true,p2(X2,X1),true),true),
inference(cp,[status(thm)],[t67,t98]) ).
cnf(t11528,plain,
true = ifeq(p2(X1,X2),true,p2(X2,X1),true),
inference(step,[status(thm)],[t100,t62]) ).
cnf(t538,plain,
ifeq(p2(X1,X2),true,p2(X2,X1),true) = true,
inference(orient,[status(thm)],[t11528]) ).
cnf(f49,negated_conjecture,
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_50) ).
fof(f49_nnf,plain,
! [X35] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [X35] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c49,plain,
( ~ p25(c32,X0)
| ~ p25(X0,c33)
| p2(f11(f4(X0),c34),f11(f4(c32),c34)) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(t57,plain,
ifeq(p25(X1,c33),true,ifeq(p25(c32,X1),true,p2(f11(f4(X1),c34),f11(f4(c32),c34)),true),true) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(t82,plain,
ifeq(p25(X1,c33),true,ifeq(p25(c32,X1),true,p2(f11(f4(X1),c34),f11(f4(c32),c34)),true),true) = true,
inference(orient,[status(thm)],[t57]) ).
cnf(f10,negated_conjecture,
p25(c36,c33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25_11) ).
fof(f10_nnf,plain,
p25(c36,c33),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
p25(c36,c33),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t13,plain,
p25(c36,c33) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t188,plain,
p25(c36,c33) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t191,plain,
true = ifeq(true,true,ifeq(p25(c32,c36),true,p2(f11(f4(c36),c34),f11(f4(c32),c34)),true),true),
inference(cp,[status(thm)],[t82,t188]) ).
cnf(t11548,plain,
true = ifeq(p25(c32,c36),true,p2(f11(f4(c36),c34),f11(f4(c32),c34)),true),
inference(step,[status(thm)],[t191,t62]) ).
cnf(f12,negated_conjecture,
p25(c32,c36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25_13) ).
fof(f12_nnf,plain,
p25(c32,c36),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
p25(c32,c36),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t12,plain,
p25(c32,c36) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t176,plain,
p25(c32,c36) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t11549,plain,
true = ifeq(true,true,p2(f11(f4(c36),c34),f11(f4(c32),c34)),true),
inference(step,[status(thm)],[t11548,t176]) ).
cnf(t11550,plain,
true = p2(f11(f4(c36),c34),f11(f4(c32),c34)),
inference(step,[status(thm)],[t11549,t62]) ).
cnf(t829,plain,
p2(f11(f4(c36),c34),f11(f4(c32),c34)) = true,
inference(orient,[status(thm)],[t11550]) ).
cnf(t830,plain,
true = ifeq(true,true,p2(f11(f4(c32),c34),f11(f4(c36),c34)),true),
inference(cp,[status(thm)],[t538,t829]) ).
cnf(t11569,plain,
true = p2(f11(f4(c32),c34),f11(f4(c36),c34)),
inference(step,[status(thm)],[t830,t62]) ).
cnf(t873,plain,
p2(f11(f4(c32),c34),f11(f4(c36),c34)) = true,
inference(orient,[status(thm)],[t11569]) ).
cnf(t11480,plain,
true = ifeq(true,true,p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),true),
inference(cp,[status(thm)],[t11479,t873]) ).
cnf(t12087,plain,
true = p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(step,[status(thm)],[t11480,t62]) ).
cnf(f18,negated_conjecture,
~ p2(X96,f18(X96,f9(f17(c31)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_19) ).
fof(f18_nnf,plain,
! [X96] : ~ p2(X96,f18(X96,f9(f17(c31)))),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X96] : ~ p2(X96,f18(X96,f9(f17(c31)))),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ p2(X0,f18(X0,f9(f17(c31)))),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t22,plain,
p2(X1,f18(X1,f9(f17(c31)))) = false,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t261,plain,
p2(X1,f18(X1,f9(f17(c31)))) = false,
inference(orient,[status(thm)],[t22]) ).
cnf(t12088,plain,
true = false,
inference(step,[status(thm)],[t12087,t261]) ).
cnf(t11484,plain,
false = true,
inference(orient,[status(thm)],[t12088]) ).
cnf(f42,negated_conjecture,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_43) ).
fof(f42_nnf,plain,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c18,c42]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t11484]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN685-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 02:07:39 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.28/3.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.28/3.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------