%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO654+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 01:18:24 PM UTC 2026
% Result : Theorem 75.95s 25.93s
% Output : Proof 75.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 156 ( 84 unt; 0 def)
% Number of atoms : 308 ( 79 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 242 ( 90 ~; 84 |; 49 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 19 ( 19 usr; 18 con; 0-4 aty)
% Number of variables : 408 ( 0 sgn 247 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( perp(C,E,E,H)
& circle(A,B,G,NWPNT9)
& coll(B,E,G)
& circle(A,D,F,NWPNT8)
& coll(D,E,F)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(H,E,G,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE0228) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( perp(C,E,E,H)
& circle(A,B,G,NWPNT9)
& coll(B,E,G)
& circle(A,D,F,NWPNT8)
& coll(D,E,F)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(H,E,G,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ~ para(H,E,G,F)
& perp(C,E,E,H)
& circle(A,B,G,NWPNT9)
& coll(B,E,G)
& circle(A,D,F,NWPNT8)
& coll(D,E,F)
& circle(C,B,E,NWPNT7)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk27,sk24,sk26,sk25)
& perp(sk22,sk24,sk24,sk27)
& circle(sk20,sk21,sk26,sk36)
& coll(sk21,sk24,sk26)
& circle(sk20,sk23,sk25,sk35)
& coll(sk23,sk24,sk25)
& circle(sk22,sk21,sk24,sk34)
& circle(sk22,sk21,sk23,sk33)
& circle(sk20,sk21,sk23,sk32)
& circle(sk22,sk21,sk30,sk31)
& circle(sk20,sk21,sk28,sk29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32,sk33,sk34,sk35,sk36])],[f94_nnf]) ).
cnf(c122,plain,
perp(sk22,sk24,sk24,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
perp(sk22,sk24,sk24,sk27) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h123,plain,
perp(sk24,sk27,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi122]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h125,plain,
para(sk22,sk24,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi122,h123]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h566,plain,
eqangle(sk22,sk24,V0,V1,sk22,sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h125]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h130,plain,
coll(sk22,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi66,h125]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h132,plain,
coll(sk24,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h130,h130]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c118,plain,
coll(sk23,sk24,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk23,sk24,sk25) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h1,plain,
coll(sk24,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi118]) ).
cnf(h8,plain,
coll(sk25,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1,h1]) ).
cnf(h21,plain,
coll(sk24,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(h136,plain,
coll(sk25,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h21,h132]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h145,plain,
coll(sk25,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h136]) ).
cnf(h165,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h145,h145]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h2778,plain,
cyclic(sk24,sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h566,h165]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h2796,plain,
cyclic(sk24,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2778]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X1,X0,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h2825,plain,
cyclic(sk22,sk24,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi15,h2796]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h2881,plain,
cyclic(sk22,sk24,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2825]) ).
fof(f16,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
fof(f16_nnf,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,cyclic(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h3015,plain,
cyclic(sk24,sk22,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2881,h2881]) ).
cnf(h3849,plain,
cyclic(sk24,sk25,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi14,h3015]) ).
cnf(h134,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h132,h132]) ).
cnf(h2781,plain,
cyclic(sk24,sk24,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h566,h134]) ).
cnf(h2802,plain,
cyclic(sk24,sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2781]) ).
cnf(h2836,plain,
cyclic(sk22,sk24,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi15,h2802]) ).
cnf(h2913,plain,
cyclic(sk22,sk24,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2836]) ).
cnf(h3188,plain,
cyclic(sk24,sk22,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2881,h2913]) ).
cnf(h4935,plain,
cyclic(sk24,sk25,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi14,h3188]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi43,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,ifeq(cyclic(X0,X1,X2,X5),true,ifeq(eqangle(X2,X0,X2,X1,X5,X3,X5,X4),true,cong(X0,X1,X3,X4),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(h8159,plain,
cong(sk24,sk25,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi43,h4935,h3849,h2778,h566]) ).
cnf(c120,plain,
coll(sk21,sk24,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk21,sk24,sk26) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h4,plain,
coll(sk24,sk21,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi120]) ).
cnf(h14,plain,
coll(sk26,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
cnf(h30,plain,
coll(sk24,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h14,h14]) ).
cnf(h135,plain,
coll(sk26,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h30,h132]) ).
cnf(h144,plain,
coll(sk26,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h135]) ).
cnf(h154,plain,
coll(sk22,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h144,h144]) ).
cnf(h2779,plain,
cyclic(sk24,sk26,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h566,h154]) ).
cnf(h2799,plain,
cyclic(sk24,sk22,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi14,h2779]) ).
cnf(h2831,plain,
cyclic(sk22,sk24,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi15,h2799]) ).
cnf(h2897,plain,
cyclic(sk22,sk24,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2831]) ).
cnf(h3086,plain,
cyclic(sk24,sk22,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2897,h2897]) ).
cnf(h4237,plain,
cyclic(sk24,sk26,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi14,h3086]) ).
cnf(h3187,plain,
cyclic(sk24,sk22,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi16,h2897,h2913]) ).
cnf(h4933,plain,
cyclic(sk24,sk26,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi14,h3187]) ).
cnf(h8157,plain,
cong(sk24,sk26,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi43,h4933,h4237,h2779,h566]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi56,axiom,
ifeq(cong(X0,X1,X2,X1),true,ifeq(cong(X0,X3,X2,X3),true,perp(X0,X2,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(h14623,plain,
perp(sk24,sk24,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi56,h8157,h8159]) ).
cnf(h143,plain,
coll(sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h134]) ).
cnf(h153,plain,
coll(sk24,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h130,h143]) ).
cnf(h152,plain,
coll(sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h143,h143]) ).
cnf(h2780,plain,
cyclic(sk24,sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h566,h152]) ).
cnf(h2837,plain,
cyclic(sk24,sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi13,h2802]) ).
cnf(h2915,plain,
cong(sk24,sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi43,h2837,h2780,h2780,h566]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(hi67,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(coll(X0,X1,X2),true,midp(X0,X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h3197,plain,
midp(sk24,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi67,h2915,h153]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(hi64,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X1,X3,X2,X4),true,ifeq(para(X1,X4,X2,X3),true,midp(X0,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h3209,plain,
midp(sk24,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi64,h3197,h125,h125]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h3225,plain,
cong(sk24,sk24,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi68,h3209]) ).
cnf(h126,plain,
para(sk24,sk27,sk24,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi8,h123,hi122]) ).
cnf(h3226,plain,
midp(sk24,sk27,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi64,h3209,h126,h126]) ).
cnf(h3291,plain,
cong(sk24,sk27,sk24,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi68,h3226]) ).
cnf(h5533,plain,
perp(sk24,sk24,sk27,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi56,h3291,h3225]) ).
cnf(h9891,plain,
perp(sk27,sk24,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,h5533]) ).
cnf(t36,plain,
para(sk27,sk24,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,h9891,h14623]) ).
cnf(t2157,plain,
para(sk27,sk24,sk26,sk25) = true,
inference(orient,[status(thm)],[t36]) ).
cnf(c123,plain,
~ para(sk27,sk24,sk26,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk27,sk24,sk26,sk25) != true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2157]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO654+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.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
% 0.28/16.27 % CPULimit : 300
% 0.28/16.27 % WCLimit : 300
% 0.28/16.27 % DateTime : Wed Sep 23 12:40:19 UTC 2026
% 0.28/16.27 % CPUTime :
% 0.28/16.27 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 75.95/25.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 75.95/25.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------