%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN651-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 03:35:24 PM UTC 2026
% Result : Unsatisfiable 3.07s 0.87s
% Output : Proof 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 39 unt; 0 def)
% Number of atoms : 95 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 110 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,negated_conjecture,
p23(f5(f7(f10(c24,f12(c25,c26)),c27),c30),c29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_26) ).
fof(f25_nnf,plain,
p23(f5(f7(f10(c24,f12(c25,c26)),c27),c30),c29),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
p23(f5(f7(f10(c24,f12(c25,c26)),c27),c30),c29),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,negated_conjecture,
p23(f5(f7(f10(c24,f12(c25,c26)),c27),c30),c29) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h2,plain,
p23(f5(f7(f10(c24,f12(c25,c26)),c27),c30),c29) = true,
inference(hyper_resolution,[status(thm)],[hi25]) ).
cnf(f44,negated_conjecture,
( ~ p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48)
| p23(f5(f7(f10(c24,X46),X45),X47),f14(f16(f18(f20(c31,X46),X47),X45),X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_45) ).
fof(f44_nnf,plain,
! [X46,X45,X47,X48] :
( ~ p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48)
| p23(f5(f7(f10(c24,X46),X45),X47),f14(f16(f18(f20(c31,X46),X47),X45),X48)) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [X46,X45,X47,X48] :
( ~ p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48)
| p23(f5(f7(f10(c24,X46),X45),X47),f14(f16(f18(f20(c31,X46),X47),X45),X48)) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( ~ p23(f5(f7(f10(c24,f12(c25,X0)),X1),X2),X3)
| p23(f5(f7(f10(c24,X0),X1),X2),f14(f16(f18(f20(c31,X0),X2),X1),X3)) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi43,negated_conjecture,
ifeq(p23(f5(f7(f10(c24,f12(c25,X0)),X1),X2),X3),true,p23(f5(f7(f10(c24,X0),X1),X2),f14(f16(f18(f20(c31,X0),X2),X1),X3)),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h6,plain,
p23(f5(f7(f10(c24,c26),c27),c30),f14(f16(f18(f20(c31,c26),c30),c27),c29)) = true,
inference(hyper_resolution,[status(thm)],[hi43,h2]) ).
cnf(f12,negated_conjecture,
p23(f5(c27,c28),c30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_13) ).
fof(f12_nnf,plain,
p23(f5(c27,c28),c30),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
p23(f5(c27,c28),c30),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,negated_conjecture,
p23(f5(c27,c28),c30) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h3,plain,
p23(f5(c27,c28),c30) = true,
inference(hyper_resolution,[status(thm)],[hi12]) ).
cnf(f43,negated_conjecture,
( ~ p23(f5(f7(f10(c24,c26),c27),X52),X50)
| ~ p23(f5(c27,X49),X52)
| p23(f5(f7(f10(c24,f12(c25,c26)),c27),X49),X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_44) ).
fof(f43_nnf,plain,
! [X49,X50,X52] :
( ~ p23(f5(f7(f10(c24,c26),c27),X52),X50)
| ~ p23(f5(c27,X49),X52)
| p23(f5(f7(f10(c24,f12(c25,c26)),c27),X49),X50) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [X49,X50,X52] :
( ~ p23(f5(f7(f10(c24,c26),c27),X52),X50)
| ~ p23(f5(c27,X49),X52)
| p23(f5(f7(f10(c24,f12(c25,c26)),c27),X49),X50) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( ~ p23(f5(f7(f10(c24,c26),c27),X2),X1)
| ~ p23(f5(c27,X0),X2)
| p23(f5(f7(f10(c24,f12(c25,c26)),c27),X0),X1) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(p23(f5(c27,X0),X1),true,ifeq(p23(f5(f7(f10(c24,c26),c27),X1),X2),true,p23(f5(f7(f10(c24,f12(c25,c26)),c27),X0),X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(h7,plain,
p23(f5(f7(f10(c24,f12(c25,c26)),c27),c28),f14(f16(f18(f20(c31,c26),c30),c27),c29)) = true,
inference(hyper_resolution,[status(thm)],[hi42,h3,h6]) ).
cnf(f40,negated_conjecture,
( ~ p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48)
| p23(f5(X45,f14(f16(f18(f20(c31,X46),X47),X45),X48)),X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_41) ).
fof(f40_nnf,plain,
! [X45,X46,X47,X48] :
( ~ p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48)
| p23(f5(X45,f14(f16(f18(f20(c31,X46),X47),X45),X48)),X48) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [X45,X46,X47,X48] :
( ~ p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48)
| p23(f5(X45,f14(f16(f18(f20(c31,X46),X47),X45),X48)),X48) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( ~ p23(f5(f7(f10(c24,f12(c25,X1)),X0),X2),X3)
| p23(f5(X0,f14(f16(f18(f20(c31,X1),X2),X0),X3)),X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi39,negated_conjecture,
ifeq(p23(f5(f7(f10(c24,f12(c25,X0)),X1),X2),X3),true,p23(f5(X1,f14(f16(f18(f20(c31,X0),X2),X1),X3)),X3),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h4,plain,
p23(f5(c27,f14(f16(f18(f20(c31,c26),c30),c27),c29)),c29) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi25]) ).
cnf(f5,negated_conjecture,
p3(X56,X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_6) ).
fof(f5_nnf,plain,
! [X56] : p3(X56,X56),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X56] : p3(X56,X56),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
p3(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
p3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h1,plain,
p3(c29,c29) = true,
inference(hyper_resolution,[status(thm)],[hi5]) ).
cnf(f26,negated_conjecture,
( ~ p23(X43,X44)
| ~ p4(X43,X41)
| ~ p3(X44,X42)
| p23(X41,X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_27) ).
fof(f26_nnf,plain,
! [X41,X42,X44,X43] :
( ~ p23(X43,X44)
| ~ p4(X43,X41)
| ~ p3(X44,X42)
| p23(X41,X42) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X41,X42,X44,X43] :
( ~ p23(X43,X44)
| ~ p4(X43,X41)
| ~ p3(X44,X42)
| p23(X41,X42) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( ~ p23(X3,X2)
| ~ p4(X3,X0)
| ~ p3(X2,X1)
| p23(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi26,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p4(X2,X3),true,ifeq(p23(X2,X0),true,p23(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(f4,negated_conjecture,
p4(X63,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_5) ).
fof(f4_nnf,plain,
! [X63] : p4(X63,X63),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X63] : p4(X63,X63),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p4(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
p4(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h5,plain,
p23(f5(c27,f14(f16(f18(f20(c31,c26),c30),c27),c29)),c29) = true,
inference(hyper_resolution,[status(thm)],[hi26,h1,hi4,h4]) ).
cnf(f42,negated_conjecture,
( ~ p23(f5(f7(f10(c24,X46),X45),X47),X51)
| ~ p23(f5(X45,X51),X48)
| p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_43) ).
fof(f42_nnf,plain,
! [X46,X45,X47,X48,X51] :
( ~ p23(f5(f7(f10(c24,X46),X45),X47),X51)
| ~ p23(f5(X45,X51),X48)
| p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [X46,X45,X47,X48,X51] :
( ~ p23(f5(f7(f10(c24,X46),X45),X47),X51)
| ~ p23(f5(X45,X51),X48)
| p23(f5(f7(f10(c24,f12(c25,X46)),X45),X47),X48) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( ~ p23(f5(f7(f10(c24,X0),X1),X2),X4)
| ~ p23(f5(X1,X4),X3)
| p23(f5(f7(f10(c24,f12(c25,X0)),X1),X2),X3) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi41,negated_conjecture,
ifeq(p23(f5(X0,X1),X2),true,ifeq(p23(f5(f7(f10(c24,X3),X0),X4),X1),true,p23(f5(f7(f10(c24,f12(c25,X3)),X0),X4),X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(t15,plain,
p23(f5(f7(f10(c24,f12(c25,f12(c25,c26))),c27),c28),c29) = true,
inference(hyper_resolution,[status(thm)],[hi41,h5,h7]) ).
cnf(t81,plain,
p23(f5(f7(f10(c24,f12(c25,f12(c25,c26))),c27),c28),c29) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(f27,negated_conjecture,
~ p23(f5(f7(f10(c24,f12(c25,f12(c25,c26))),c27),c28),c29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p23_28) ).
fof(f27_nnf,plain,
~ p23(f5(f7(f10(c24,f12(c25,f12(c25,c26))),c27),c28),c29),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
~ p23(f5(f7(f10(c24,f12(c25,f12(c25,c26))),c27),c28),c29),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ p23(f5(f7(f10(c24,f12(c25,f12(c25,c26))),c27),c28),c29),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(goal_0,negated_conjecture,
p23(f5(f7(f10(c24,f12(c25,f12(c25,c26))),c27),c28),c29) != true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t81]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN651-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 01:59:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.07/0.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.07/0.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------