%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO591+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:18:14 PM UTC 2026
% Result : Theorem 180.00s 23.29s
% Output : Proof 180.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 22
% Syntax : Number of formulae : 209 ( 121 unt; 0 def)
% Number of atoms : 381 ( 114 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 286 ( 114 ~; 108 |; 41 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 474 ( 0 sgn 285 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/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]) ).
fof(f94,conjecture,
! [O,A,B,C,E,D,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(D,C,E)
& perp(O,C,C,E)
& coll(C,A,B)
& perp(O,A,A,D)
& perp(O,B,B,E)
& circle(O,A,B,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2) )
=> cong(O,E,O,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416053) ).
fof(f94_neg,negated_conjecture,
~ ! [O,A,B,C,E,D,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(D,C,E)
& perp(O,C,C,E)
& coll(C,A,B)
& perp(O,A,A,D)
& perp(O,B,B,E)
& circle(O,A,B,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2) )
=> cong(O,E,O,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [O,A,B,C,E,D,NWPNT1,NWPNT2,NWPNT3] :
( ~ cong(O,E,O,D)
& coll(D,C,E)
& perp(O,C,C,E)
& coll(C,A,B)
& perp(O,A,A,D)
& perp(O,B,B,E)
& circle(O,A,B,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk20,sk24,sk20,sk25)
& coll(sk25,sk23,sk24)
& perp(sk20,sk23,sk23,sk24)
& coll(sk23,sk21,sk22)
& perp(sk20,sk21,sk21,sk25)
& perp(sk20,sk22,sk22,sk24)
& circle(sk20,sk21,sk22,sk28)
& circle(sk20,sk21,sk26,sk27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c117,plain,
coll(sk23,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk23,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h0,plain,
coll(sk22,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(h6,plain,
coll(sk23,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,h0]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/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(c119,plain,
coll(sk25,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
coll(sk25,sk23,sk24) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h5,plain,
coll(sk25,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi119]) ).
cnf(h16,plain,
coll(sk23,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h5]) ).
cnf(h35,plain,
coll(sk25,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h16,h6]) ).
cnf(h58,plain,
coll(sk25,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h35]) ).
cnf(h76,plain,
coll(sk24,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi119,h58]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/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]) ).
cnf(c115,plain,
perp(sk20,sk22,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
perp(sk20,sk22,sk22,sk24) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h123,plain,
perp(sk22,sk24,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi115]) ).
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/sandbox/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(h129,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi115,h123]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/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(h144,plain,
coll(sk20,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi66,h129]) ).
cnf(h146,plain,
coll(sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h144,h144]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/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(h4,plain,
coll(sk23,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi119]) ).
cnf(h14,plain,
coll(sk24,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
cnf(h30,plain,
coll(sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h14,h14]) ).
cnf(h55,plain,
coll(sk24,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h30,h6]) ).
cnf(h66,plain,
coll(sk24,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h55]) ).
cnf(h116,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h66,h66]) ).
cnf(h149,plain,
coll(sk24,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h116,h146]) ).
cnf(h158,plain,
coll(sk24,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h149]) ).
cnf(h176,plain,
coll(sk20,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h158,h76]) ).
cnf(h148,plain,
coll(sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h146,h146]) ).
cnf(h157,plain,
coll(sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h148]) ).
cnf(h167,plain,
coll(sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h144,h157]) ).
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/sandbox/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(h557,plain,
eqangle(sk20,sk22,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h129]) ).
cnf(h166,plain,
coll(sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h157,h157]) ).
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/sandbox/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(h5576,plain,
cyclic(sk22,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h557,h166]) ).
cnf(h5577,plain,
cyclic(sk22,sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h557,h148]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/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(h5595,plain,
cyclic(sk22,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h5577]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/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(h5622,plain,
cyclic(sk22,sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi13,h5595]) ).
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/sandbox/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(h5682,plain,
cong(sk22,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi43,h5622,h5576,h5576,h557]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/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(h5855,plain,
midp(sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi67,h5682,h167]) ).
cnf(c118,plain,
perp(sk20,sk23,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
perp(sk20,sk23,sk23,sk24) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h127,plain,
perp(sk23,sk24,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi118]) ).
cnf(h140,plain,
para(sk23,sk24,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,h127,hi118]) ).
cnf(h139,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi118,h127]) ).
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/sandbox/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(h5867,plain,
midp(sk22,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi64,h5855,h139,h139]) ).
cnf(h5884,plain,
midp(sk22,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi64,h5867,h140,h140]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h6047,plain,
para(sk24,sk20,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi63,h5884,h5855]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h9596,plain,
para(sk24,sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi3,h6047]) ).
cnf(h74,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h58,h58]) ).
cnf(h154,plain,
coll(sk20,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h146,h74]) ).
cnf(h163,plain,
coll(sk20,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h154]) ).
cnf(h153,plain,
coll(sk20,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h146,h116]) ).
cnf(h162,plain,
coll(sk20,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h153]) ).
cnf(h216,plain,
coll(sk24,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h162,h163]) ).
fof(f57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD57) ).
fof(f57_nnf,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [A,P,B,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
( perp(X2,X0,X0,X3)
| ~ cyclic(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(hi57,axiom,
ifeq(cong(X0,X1,X2,X1),true,ifeq(cong(X0,X3,X2,X3),true,ifeq(cyclic(X0,X2,X1,X3),true,perp(X1,X0,X0,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(h5856,plain,
perp(sk20,sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi57,h5682,h5682,h5577]) ).
cnf(h8014,plain,
para(sk22,sk24,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h123,h5856]) ).
cnf(h34,plain,
coll(sk22,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h6,h16]) ).
cnf(h57,plain,
coll(sk22,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h34]) ).
cnf(h7,plain,
coll(sk22,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0]) ).
cnf(h70,plain,
coll(sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h7,h57]) ).
cnf(h5869,plain,
midp(sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi64,h5855,h129,h129]) ).
cnf(c116,plain,
perp(sk20,sk21,sk21,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
perp(sk20,sk21,sk21,sk25) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h125,plain,
perp(sk21,sk25,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi116]) ).
cnf(h135,plain,
para(sk21,sk25,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi8,h125,hi116]) ).
cnf(h134,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi116,h125]) ).
cnf(h5868,plain,
midp(sk22,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi64,h5855,h134,h134]) ).
cnf(h5906,plain,
midp(sk22,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi64,h5868,h135,h135]) ).
cnf(h6109,plain,
para(sk25,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi63,h5906,h5869]) ).
cnf(h6105,plain,
para(sk22,sk25,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi63,h5869,h5906]) ).
cnf(h72,plain,
coll(sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h57,h7]) ).
cnf(h3,plain,
coll(sk24,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi119,hi119]) ).
cnf(h12,plain,
coll(sk25,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h3,h3]) ).
cnf(h27,plain,
coll(sk25,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h12]) ).
cnf(h50,plain,
coll(sk25,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h27,h5]) ).
cnf(h75,plain,
coll(sk25,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h50,h58]) ).
cnf(h1,plain,
coll(sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi117]) ).
cnf(h8,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1,h1]) ).
cnf(h21,plain,
coll(sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(h42,plain,
coll(sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h21]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h131,plain,
perp(sk22,sk24,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi6,h123]) ).
cnf(h236,plain,
perp(sk22,sk20,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,h131]) ).
cnf(h251,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h236,h131]) ).
fof(f45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD45) ).
fof(f45_nnf,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [E,A,B,F,C] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( midp(X4,X0,X2)
| ~ coll(X4,X0,X2)
| ~ para(X3,X4,X1,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi45,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X0,X3,X2,X4),true,ifeq(coll(X3,X1,X4),true,midp(X3,X1,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(h5945,plain,
midp(sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi45,h5869,h251,h157]) ).
cnf(h6192,plain,
midp(sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi45,h5945,h134,h42]) ).
cnf(h6601,plain,
midp(sk25,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi45,h6192,h135,h75]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h6868,plain,
midp(sk25,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi10,h6601]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/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(h7173,plain,
cong(sk25,sk25,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi68,h6868]) ).
cnf(h6867,plain,
cong(sk25,sk22,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi68,h6601]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(cong(X0,X1,X2,X3),true,ifeq(cong(X2,X3,X4,X5),true,cong(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h11134,plain,
cong(sk25,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi24,h6867,h7173]) ).
cnf(h63835,plain,
midp(sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi67,h11134,h72]) ).
cnf(h64831,plain,
midp(sk25,sk25,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi64,h63835,h6105,h6105]) ).
cnf(h65909,plain,
midp(sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi45,h64831,h6109,h70]) ).
cnf(h74419,plain,
midp(sk24,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi45,h65909,h8014,h216]) ).
cnf(h82346,plain,
midp(sk20,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi45,h74419,h9596,h176]) ).
cnf(h83506,plain,
midp(sk20,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi10,h82346]) ).
cnf(t24,plain,
cong(sk20,sk24,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi68,h83506]) ).
cnf(t1542,plain,
cong(sk20,sk24,sk20,sk25) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(c120,plain,
~ cong(sk20,sk24,sk20,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cong(sk20,sk24,sk20,sk25) != true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1542]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO591+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n001.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 12:35:19 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 180.00/23.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 180.00/23.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------