%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO616+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 : n020.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 01:18:18 PM UTC 2026
% Result : Theorem 73.82s 11.08s
% Output : Proof 73.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 23
% Syntax : Number of formulae : 176 ( 65 unt; 0 def)
% Number of atoms : 368 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 318 ( 126 ~; 122 |; 46 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 500 ( 15 sgn 329 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f94,conjecture,
! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618078) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ~ perp(E,K,K,N)
& circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk25,sk26,sk26,sk28)
& circle(sk28,sk26,sk24,sk27)
& coll(sk27,sk23,sk24)
& perp(sk27,sk20,sk23,sk24)
& coll(sk26,sk20,sk21)
& perp(sk26,sk25,sk20,sk21)
& circle(sk23,sk20,sk25,sk29)
& coll(sk25,sk23,sk24)
& midp(sk24,sk22,sk21)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29])],[f94_nnf]) ).
cnf(c114,plain,
midp(sk24,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p636,plain,
cong(sk24,sk22,sk24,sk21),
inference(resolution,[status(thm)],[c68,c114]) ).
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(p653,plain,
( cong(sk24,sk22,X0,X1)
| ~ cong(sk24,sk21,X0,X1) ),
inference(resolution,[status(thm)],[p636,c24]) ).
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(p157,plain,
midp(sk24,sk21,sk22),
inference(resolution,[status(thm)],[c10,c114]) ).
cnf(p637,plain,
cong(sk24,sk21,sk24,sk22),
inference(resolution,[status(thm)],[c68,p157]) ).
cnf(p1841,plain,
cong(sk24,sk22,sk24,sk22),
inference(resolution,[status(thm)],[p653,p637]) ).
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(p1848,plain,
( midp(sk24,sk22,sk22)
| ~ coll(sk24,sk22,sk22) ),
inference(resolution,[status(thm)],[p1841,c67]) ).
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(p136,plain,
( coll(X2,X2,X0)
| ~ coll(X0,X1,X2) ),
inference(factoring,[status(thm)],[c2]) ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD69) ).
fof(f69_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f69]) ).
fof(f69_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c69,plain,
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(p159,plain,
coll(sk24,sk21,sk22),
inference(resolution,[status(thm)],[c69,p157]) ).
cnf(p222,plain,
coll(sk22,sk22,sk24),
inference(resolution,[status(thm)],[p136,p159]) ).
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(p262,plain,
coll(sk22,sk24,sk22),
inference(resolution,[status(thm)],[p222,c0]) ).
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(p313,plain,
coll(sk24,sk22,sk22),
inference(resolution,[status(thm)],[p262,c1]) ).
cnf(p2295,plain,
midp(sk24,sk22,sk22),
inference(resolution,[status(thm)],[p1848,p313]) ).
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(p605,plain,
( midp(X0,X3,X3)
| ~ para(X1,X3,X2,X3)
| ~ midp(X0,X1,X2) ),
inference(factoring,[status(thm)],[c64]) ).
cnf(p2312,plain,
( midp(sk24,X0,X0)
| ~ para(sk22,X0,sk22,X0) ),
inference(resolution,[status(thm)],[p2295,p605]) ).
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(c117,plain,
perp(sk26,sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p177,plain,
( para(sk26,sk25,X0,X1)
| ~ perp(sk20,sk21,X0,X1) ),
inference(resolution,[status(thm)],[c8,c117]) ).
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(p170,plain,
perp(sk20,sk21,sk26,sk25),
inference(resolution,[status(thm)],[c7,c117]) ).
cnf(p1205,plain,
para(sk26,sk25,sk26,sk25),
inference(resolution,[status(thm)],[p177,p170]) ).
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(p1323,plain,
eqangle(sk26,sk25,X0,X1,sk26,sk25,X0,X1),
inference(resolution,[status(thm)],[p1205,c39]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p2080,plain,
eqangle(X0,X1,sk26,sk25,X0,X1,sk26,sk25),
inference(resolution,[status(thm)],[p1323,c18]) ).
fof(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p2699,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p2080,c38]) ).
cnf(p16120,plain,
midp(sk24,X0,X0),
inference(resolution,[status(thm)],[p2312,p2699]) ).
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(p597,plain,
( para(sk22,X0,sk21,X1)
| ~ midp(sk24,X0,X1) ),
inference(resolution,[status(thm)],[c63,c114]) ).
cnf(p16135,plain,
para(sk22,X0,sk21,X0),
inference(resolution,[status(thm)],[p16120,p597]) ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD10) ).
fof(f9_nnf,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p16184,plain,
( perp(sk22,X0,X1,X2)
| ~ perp(sk21,X0,X1,X2) ),
inference(resolution,[status(thm)],[p16135,c9]) ).
cnf(p16126,plain,
cong(sk24,X0,sk24,X0),
inference(resolution,[status(thm)],[p16120,c68]) ).
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/sandbox/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(p16158,plain,
( perp(sk24,sk24,X1,X0)
| ~ cong(sk24,X0,sk24,X0) ),
inference(resolution,[status(thm)],[p16126,c56]) ).
cnf(p47934,plain,
perp(sk24,sk24,X0,X1),
inference(resolution,[status(thm)],[p16158,p16126]) ).
cnf(p47946,plain,
perp(X0,X1,sk24,sk24),
inference(resolution,[status(thm)],[p47934,c7]) ).
fof(f44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD44) ).
fof(f44_nnf,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [E,A,B,F,C] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( para(X3,X4,X1,X2)
| ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p416,plain,
( para(X0,X0,X2,X2)
| ~ midp(X0,X1,X2) ),
inference(factoring,[status(thm)],[c44]) ).
cnf(p1511,plain,
para(sk24,sk24,sk21,sk21),
inference(resolution,[status(thm)],[p416,c114]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p1529,plain,
para(sk21,sk21,sk24,sk24),
inference(resolution,[status(thm)],[p1511,c4]) ).
cnf(p1545,plain,
eqangle(sk21,sk21,X0,X1,sk24,sk24,X0,X1),
inference(resolution,[status(thm)],[p1529,c39]) ).
cnf(p2184,plain,
eqangle(X0,X1,sk21,sk21,X0,X1,sk24,sk24),
inference(resolution,[status(thm)],[p1545,c18]) ).
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD74) ).
fof(f74_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(p2902,plain,
( perp(X0,X1,sk21,sk21)
| ~ perp(X0,X1,sk24,sk24) ),
inference(resolution,[status(thm)],[p2184,c74]) ).
cnf(p47967,plain,
perp(X0,X1,sk21,sk21),
inference(resolution,[status(thm)],[p47946,p2902]) ).
cnf(p48023,plain,
perp(sk21,sk21,X0,X1),
inference(resolution,[status(thm)],[p47967,c7]) ).
cnf(p48315,plain,
perp(sk22,sk21,X0,X1),
inference(resolution,[status(thm)],[p16184,p48023]) ).
fof(f53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD53) ).
fof(f53_nnf,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [O,A,B,C] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
( perp(X0,X1,X1,X2)
| ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(c113,plain,
circle(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p510,plain,
( perp(sk20,sk21,sk21,sk22)
| ~ coll(sk23,sk20,sk22) ),
inference(resolution,[status(thm)],[c53,c113]) ).
cnf(c115,plain,
coll(sk25,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p205,plain,
coll(sk24,sk24,sk25),
inference(resolution,[status(thm)],[p136,c115]) ).
cnf(p228,plain,
( coll(sk25,X0,sk24)
| ~ coll(sk24,sk24,X0) ),
inference(resolution,[status(thm)],[p205,c2]) ).
cnf(p158,plain,
coll(sk24,sk22,sk21),
inference(resolution,[status(thm)],[c69,c114]) ).
cnf(p162,plain,
coll(sk22,sk24,sk21),
inference(resolution,[status(thm)],[p158,c1]) ).
cnf(p166,plain,
coll(sk22,sk21,sk24),
inference(resolution,[status(thm)],[p162,c0]) ).
cnf(p225,plain,
coll(sk24,sk24,sk22),
inference(resolution,[status(thm)],[p136,p166]) ).
cnf(p382,plain,
coll(sk25,sk22,sk24),
inference(resolution,[status(thm)],[p228,p225]) ).
cnf(p384,plain,
coll(sk25,sk24,sk22),
inference(resolution,[status(thm)],[p382,c0]) ).
cnf(p123,plain,
coll(sk25,sk24,sk23),
inference(resolution,[status(thm)],[c0,c115]) ).
cnf(p140,plain,
( coll(sk23,X0,sk25)
| ~ coll(sk25,sk24,X0) ),
inference(resolution,[status(thm)],[c2,p123]) ).
cnf(p393,plain,
coll(sk23,sk22,sk25),
inference(resolution,[status(thm)],[p384,p140]) ).
cnf(p411,plain,
coll(sk23,sk25,sk22),
inference(resolution,[status(thm)],[p393,c0]) ).
cnf(p441,plain,
( coll(sk22,X0,sk23)
| ~ coll(sk23,sk25,X0) ),
inference(resolution,[status(thm)],[p411,c2]) ).
cnf(c118,plain,
coll(sk26,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p206,plain,
coll(sk21,sk21,sk26),
inference(resolution,[status(thm)],[p136,c118]) ).
cnf(p230,plain,
( coll(sk26,X0,sk21)
| ~ coll(sk21,sk21,X0) ),
inference(resolution,[status(thm)],[p206,c2]) ).
cnf(p221,plain,
coll(sk21,sk21,sk24),
inference(resolution,[status(thm)],[p136,p158]) ).
cnf(p674,plain,
coll(sk26,sk24,sk21),
inference(resolution,[status(thm)],[p230,p221]) ).
cnf(p679,plain,
coll(sk26,sk21,sk24),
inference(resolution,[status(thm)],[p674,c0]) ).
cnf(p124,plain,
coll(sk26,sk21,sk20),
inference(resolution,[status(thm)],[c0,c118]) ).
cnf(p141,plain,
( coll(sk20,X0,sk26)
| ~ coll(sk26,sk21,X0) ),
inference(resolution,[status(thm)],[c2,p124]) ).
cnf(p697,plain,
coll(sk20,sk24,sk26),
inference(resolution,[status(thm)],[p679,p141]) ).
cnf(p731,plain,
coll(sk20,sk26,sk24),
inference(resolution,[status(thm)],[p697,c0]) ).
cnf(p858,plain,
coll(sk24,sk24,sk20),
inference(resolution,[status(thm)],[p731,p136]) ).
cnf(p962,plain,
coll(sk25,sk20,sk24),
inference(resolution,[status(thm)],[p858,p228]) ).
cnf(p1128,plain,
coll(sk25,sk24,sk20),
inference(resolution,[status(thm)],[p962,c0]) ).
cnf(p1192,plain,
coll(sk23,sk20,sk25),
inference(resolution,[status(thm)],[p1128,p140]) ).
cnf(p1229,plain,
coll(sk23,sk25,sk20),
inference(resolution,[status(thm)],[p1192,c0]) ).
cnf(p1504,plain,
coll(sk22,sk20,sk23),
inference(resolution,[status(thm)],[p441,p1229]) ).
cnf(p1508,plain,
coll(sk22,sk23,sk20),
inference(resolution,[status(thm)],[p1504,c0]) ).
cnf(p1517,plain,
coll(sk23,sk22,sk20),
inference(resolution,[status(thm)],[p1508,c1]) ).
cnf(p1524,plain,
coll(sk23,sk20,sk22),
inference(resolution,[status(thm)],[p1517,c0]) ).
cnf(p1595,plain,
perp(sk20,sk21,sk21,sk22),
inference(resolution,[status(thm)],[p510,p1524]) ).
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(p1596,plain,
perp(sk20,sk21,sk22,sk21),
inference(resolution,[status(thm)],[p1595,c6]) ).
cnf(p181,plain,
perp(sk20,sk21,sk25,sk26),
inference(resolution,[status(thm)],[p170,c6]) ).
cnf(p189,plain,
perp(sk25,sk26,sk20,sk21),
inference(resolution,[status(thm)],[p181,c7]) ).
cnf(p198,plain,
( para(sk25,sk26,X0,X1)
| ~ perp(sk20,sk21,X0,X1) ),
inference(resolution,[status(thm)],[p189,c8]) ).
cnf(p1626,plain,
para(sk25,sk26,sk22,sk21),
inference(resolution,[status(thm)],[p1596,p198]) ).
cnf(p1670,plain,
( perp(sk25,sk26,X0,X1)
| ~ perp(sk22,sk21,X0,X1) ),
inference(resolution,[status(thm)],[p1626,c9]) ).
cnf(p48527,plain,
perp(sk25,sk26,X0,X1),
inference(resolution,[status(thm)],[p48315,p1670]) ).
cnf(c122,plain,
~ perp(sk25,sk26,sk26,sk28),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p48840,plain,
$false,
inference(resolution,[status(thm)],[p48527,c122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO616+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 12:34:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 73.82/11.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.82/11.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------