%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN669-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 03:35:26 PM UTC 2026
% Result : Unsatisfiable 12.75s 2.05s
% Output : Proof 12.75s
% 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(f29,negated_conjecture,
( ~ p2(X28,X30)
| ~ p2(X28,X29)
| p2(X29,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_30) ).
fof(f29_nnf,plain,
! [X29,X30,X28] :
( ~ p2(X28,X30)
| ~ p2(X28,X29)
| p2(X29,X30) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X29,X30,X28] :
( ~ p2(X28,X30)
| ~ p2(X28,X29)
| p2(X29,X30) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(t39,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t66,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(f38,negated_conjecture,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_39) ).
fof(f38_nnf,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c38,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(t31,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t114,plain,
p2(f11(f4(c32),c34),f18(f11(f4(c36),c34),f9(f17(c31)))) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t116,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)],[t66,t114]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t61,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t6552,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)],[t116,t61]) ).
cnf(t6201,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)],[t6552]) ).
cnf(f6,negated_conjecture,
p2(X28,X28),
file('/export/starexec/sandbox2/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(t10,plain,
p2(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t97,plain,
p2(X1,X1) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t99,plain,
true = ifeq(p2(X1,X2),true,ifeq(true,true,p2(X2,X1),true),true),
inference(cp,[status(thm)],[t66,t97]) ).
cnf(t6235,plain,
true = ifeq(p2(X1,X2),true,p2(X2,X1),true),
inference(step,[status(thm)],[t99,t61]) ).
cnf(t294,plain,
ifeq(p2(X1,X2),true,p2(X2,X1),true) = true,
inference(orient,[status(thm)],[t6235]) ).
cnf(f48,negated_conjecture,
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_49) ).
fof(f48_nnf,plain,
! [X35] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [X35] :
( ~ p25(c32,X35)
| ~ p25(X35,c33)
| p2(f11(f4(X35),c34),f11(f4(c32),c34)) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c48,plain,
( ~ p25(c32,X0)
| ~ p25(X0,c33)
| p2(f11(f4(X0),c34),f11(f4(c32),c34)) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(t56,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)],[c48]) ).
cnf(t81,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)],[t56]) ).
cnf(f11,negated_conjecture,
p25(c36,c33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_12) ).
fof(f11_nnf,plain,
p25(c36,c33),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
p25(c36,c33),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t14,plain,
p25(c36,c33) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t184,plain,
p25(c36,c33) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t187,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)],[t81,t184]) ).
cnf(t6241,plain,
true = ifeq(p25(c32,c36),true,p2(f11(f4(c36),c34),f11(f4(c32),c34)),true),
inference(step,[status(thm)],[t187,t61]) ).
cnf(f12,negated_conjecture,
p25(c32,c36),
file('/export/starexec/sandbox2/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(t13,plain,
p25(c32,c36) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t172,plain,
p25(c32,c36) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t6242,plain,
true = ifeq(true,true,p2(f11(f4(c36),c34),f11(f4(c32),c34)),true),
inference(step,[status(thm)],[t6241,t172]) ).
cnf(t6243,plain,
true = p2(f11(f4(c36),c34),f11(f4(c32),c34)),
inference(step,[status(thm)],[t6242,t61]) ).
cnf(t319,plain,
p2(f11(f4(c36),c34),f11(f4(c32),c34)) = true,
inference(orient,[status(thm)],[t6243]) ).
cnf(t320,plain,
true = ifeq(true,true,p2(f11(f4(c32),c34),f11(f4(c36),c34)),true),
inference(cp,[status(thm)],[t294,t319]) ).
cnf(t6263,plain,
true = p2(f11(f4(c32),c34),f11(f4(c36),c34)),
inference(step,[status(thm)],[t320,t61]) ).
cnf(t364,plain,
p2(f11(f4(c32),c34),f11(f4(c36),c34)) = true,
inference(orient,[status(thm)],[t6263]) ).
cnf(t6202,plain,
true = ifeq(true,true,p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),true),
inference(cp,[status(thm)],[t6201,t364]) ).
cnf(t6553,plain,
true = p2(f11(f4(c36),c34),f18(f11(f4(c36),c34),f9(f17(c31)))),
inference(step,[status(thm)],[t6202,t61]) ).
cnf(f17,negated_conjecture,
~ p2(X96,f18(X96,f9(f17(c31)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_18) ).
fof(f17_nnf,plain,
! [X96] : ~ p2(X96,f18(X96,f9(f17(c31)))),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X96] : ~ p2(X96,f18(X96,f9(f17(c31)))),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
~ p2(X0,f18(X0,f9(f17(c31)))),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t21,plain,
p2(X1,f18(X1,f9(f17(c31)))) = false,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t249,plain,
p2(X1,f18(X1,f9(f17(c31)))) = false,
inference(orient,[status(thm)],[t21]) ).
cnf(t6554,plain,
true = false,
inference(step,[status(thm)],[t6553,t249]) ).
cnf(t6208,plain,
false = true,
inference(orient,[status(thm)],[t6554]) ).
cnf(f41,negated_conjecture,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_42) ).
fof(f41_nnf,plain,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
~ p2(f11(f4(f16(c32,f9(f17(c31)))),c34),f11(f4(c32),c34)),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c17,c41]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6208]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN669-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Fri Sep 25 02:02:06 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.75/2.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.75/2.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------