%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO633+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 01:18:21 PM UTC 2026
% Result : Theorem 208.88s 26.97s
% Output : Proof 208.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 94
% Number of leaves : 24
% Syntax : Number of formulae : 281 ( 189 unt; 0 def)
% Number of atoms : 453 ( 185 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 283 ( 111 ~; 105 |; 43 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 929 ( 154 sgn 349 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(t167,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t271,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t167]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t127,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t268,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t127]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t128,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t128]) ).
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(t125,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t125]) ).
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(t215,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t333,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t215]) ).
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(t180,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t180]) ).
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(t135,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t135]) ).
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/sandbox2/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(t152,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t152]) ).
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/sandbox2/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(t172,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t308,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t172]) ).
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(t153,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t346,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t153]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X4,X5,X6,X7,X0,X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
fof(f94,conjecture,
! [A,B,C,A1,S,N,G,H] :
( ( coll(H,A,C)
& perp(H,N,A,C)
& coll(G,A,B)
& perp(G,N,A,B)
& coll(N,A,A1)
& coll(S,B,C)
& eqangle(S,A,A,B,C,A,A,A1)
& midp(A1,C,B) )
=> perp(G,H,A,S) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL8110996) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,A1,S,N,G,H] :
( ( coll(H,A,C)
& perp(H,N,A,C)
& coll(G,A,B)
& perp(G,N,A,B)
& coll(N,A,A1)
& coll(S,B,C)
& eqangle(S,A,A,B,C,A,A,A1)
& midp(A1,C,B) )
=> perp(G,H,A,S) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,A1,S,N,G,H] :
( ~ perp(G,H,A,S)
& coll(H,A,C)
& perp(H,N,A,C)
& coll(G,A,B)
& perp(G,N,A,B)
& coll(N,A,A1)
& coll(S,B,C)
& eqangle(S,A,A,B,C,A,A,A1)
& midp(A1,C,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk26,sk27,sk20,sk24)
& coll(sk27,sk20,sk22)
& perp(sk27,sk25,sk20,sk22)
& coll(sk26,sk20,sk21)
& perp(sk26,sk25,sk20,sk21)
& coll(sk25,sk20,sk23)
& coll(sk24,sk21,sk22)
& eqangle(sk24,sk20,sk20,sk21,sk22,sk20,sk20,sk23)
& midp(sk23,sk22,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c114,plain,
eqangle(sk24,sk20,sk20,sk21,sk22,sk20,sk20,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
eqangle(sk24,sk20,sk20,sk21,sk22,sk20,sk20,sk23) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h10,plain,
eqangle(sk22,sk20,sk20,sk23,sk24,sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi114]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h94,plain,
eqangle(sk22,sk20,sk20,sk23,sk22,sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi21,h10,hi114]) ).
cnf(hi38,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X2,X3),true,para(X0,X1,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t64,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi38,h94]) ).
cnf(t2297,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t64]) ).
cnf(t2301,plain,
true = ifeq(true,true,eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2),true),
inference(cp,[status(thm)],[t346,t2297]) ).
cnf(t56,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t56]) ).
cnf(t31037,plain,
true = eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2),
inference(step,[status(thm)],[t2301,t256]) ).
cnf(t7754,plain,
eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t31037]) ).
cnf(t7760,plain,
true = ifeq(true,true,eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20),true),
inference(cp,[status(thm)],[t308,t7754]) ).
cnf(t31352,plain,
true = eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20),
inference(step,[status(thm)],[t7760,t256]) ).
cnf(t12205,plain,
eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20) = true,
inference(orient,[status(thm)],[t31352]) ).
cnf(t12207,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t12205]) ).
cnf(t31353,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t12207,t256]) ).
cnf(t12229,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t31353]) ).
cnf(t12246,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t333,t12229]) ).
cnf(t32939,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t12246,t256]) ).
cnf(t32940,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t32939,t12229]) ).
cnf(t32941,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t32940,t256]) ).
cnf(t27260,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t32941]) ).
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(t158,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t272,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t158]) ).
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(t240,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t357,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t240]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t151,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t151]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(c113,plain,
midp(sk23,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
midp(sk23,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h5,plain,
cong(sk23,sk22,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi113]) ).
cnf(hi23,axiom,
ifeq(cong(X0,X1,X2,X3),true,cong(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h57,plain,
cong(sk23,sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi23,h5]) ).
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/sandbox2/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(h412,plain,
cong(sk23,sk21,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi24,h57,h5]) ).
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t45,plain,
cyclic(sk21,sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi12,h412,h57,h412]) ).
cnf(t2819,plain,
cyclic(sk21,sk21,sk22,sk21) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(t2822,plain,
true = ifeq(true,true,eqangle(sk22,sk21,sk22,sk21,sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t359,t2819]) ).
cnf(t31136,plain,
true = eqangle(sk22,sk21,sk22,sk21,sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t2822,t256]) ).
cnf(t9266,plain,
eqangle(sk22,sk21,sk22,sk21,sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t31136]) ).
cnf(t9278,plain,
true = ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(cp,[status(thm)],[t357,t9266]) ).
cnf(t31137,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(step,[status(thm)],[t9278,t2819]) ).
cnf(t31138,plain,
true = ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t31137,t256]) ).
cnf(t31139,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t31138,t2819]) ).
cnf(t31140,plain,
true = ifeq(cyclic(sk21,sk21,sk22,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t31139,t256]) ).
cnf(t31141,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t31140,t2819]) ).
cnf(t31142,plain,
true = ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),
inference(step,[status(thm)],[t31141,t256]) ).
cnf(t31143,plain,
true = cong(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t31142,t256]) ).
cnf(t9279,plain,
cong(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t31143]) ).
cnf(t9289,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),true),
inference(cp,[status(thm)],[t272,t9279]) ).
cnf(t31144,plain,
true = ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t9289,t256]) ).
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(t126,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t126]) ).
cnf(h59,plain,
cyclic(sk22,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi12,h5,h5,h5]) ).
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(t46,plain,
cyclic(sk21,sk22,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi15,h59]) ).
cnf(t2803,plain,
cyclic(sk21,sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t2806,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk21,sk22,sk21,sk21,sk21,sk22),true),
inference(cp,[status(thm)],[t359,t2803]) ).
cnf(t31133,plain,
true = eqangle(sk21,sk21,sk21,sk22,sk21,sk21,sk21,sk22),
inference(step,[status(thm)],[t2806,t256]) ).
cnf(t9205,plain,
eqangle(sk21,sk21,sk21,sk22,sk21,sk21,sk21,sk22) = true,
inference(orient,[status(thm)],[t31133]) ).
cnf(t9207,plain,
true = ifeq(true,true,para(sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t314,t9205]) ).
cnf(t31134,plain,
true = para(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t9207,t256]) ).
cnf(t9218,plain,
para(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t31134]) ).
cnf(t9219,plain,
true = ifeq(true,true,coll(sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t353,t9218]) ).
cnf(t31135,plain,
true = coll(sk21,sk21,sk21),
inference(step,[status(thm)],[t9219,t256]) ).
cnf(t9239,plain,
coll(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t31135]) ).
cnf(t31145,plain,
true = ifeq(true,true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t31144,t9239]) ).
cnf(t31146,plain,
true = midp(sk21,sk21,sk21),
inference(step,[status(thm)],[t31145,t256]) ).
cnf(t9317,plain,
midp(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t31146]) ).
cnf(t27261,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t27260,t9317]) ).
cnf(t32942,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t27261,t256]) ).
cnf(t27291,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t32942]) ).
cnf(t27292,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t336,t27291]) ).
cnf(t32944,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t27292,t256]) ).
cnf(t27331,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t32944]) ).
cnf(t27344,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t27331]) ).
cnf(t32955,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t27344,t256]) ).
cnf(t32956,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t32955,t27331]) ).
cnf(t32957,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t32956,t256]) ).
cnf(t27442,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t32957]) ).
cnf(t27443,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t292,t27442]) ).
cnf(t32963,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t27443,t256]) ).
cnf(t27549,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t32963]) ).
cnf(t27556,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t27549]) ).
cnf(t32967,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t27556,t256]) ).
cnf(t32968,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t32967,t27442]) ).
cnf(t32969,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t32968,t256]) ).
cnf(t27664,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t32969]) ).
cnf(t32981,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t333,t27664]) ).
cnf(t32982,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t32981,t256]) ).
cnf(t32983,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t32982,t27664]) ).
cnf(t32984,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t32983,t256]) ).
cnf(t27671,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t32984]) ).
cnf(t28583,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t27671]) ).
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(t157,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t157]) ).
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(t121,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t263,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t121]) ).
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(t122,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t261,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t122]) ).
cnf(t12230,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t12229]) ).
cnf(t31354,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t12230,t256]) ).
cnf(t12255,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t31354]) ).
cnf(t12257,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t12255]) ).
cnf(t31355,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t12257,t256]) ).
cnf(t12298,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t31355]) ).
cnf(t12301,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t12298]) ).
cnf(t31356,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t12301,t256]) ).
cnf(t12330,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t31356]) ).
cnf(t12333,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t12330]) ).
cnf(t31357,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t12333,t256]) ).
cnf(t31358,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t31357,t12330]) ).
cnf(t31359,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t31358,t256]) ).
cnf(t12364,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t31359]) ).
cnf(t31370,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t12364]) ).
cnf(t31371,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t31370,t256]) ).
cnf(t12371,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t31371]) ).
cnf(t30342,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t12371]) ).
cnf(t22,plain,
midp(sk23,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t1837,plain,
midp(sk23,sk22,sk21) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t28606,plain,
true = ifeq(true,true,midp(sk23,X1,X2),true),
inference(cp,[status(thm)],[t28583,t1837]) ).
cnf(t33065,plain,
true = midp(sk23,X1,X2),
inference(step,[status(thm)],[t28606,t256]) ).
cnf(t28651,plain,
midp(sk23,X1,X2) = true,
inference(orient,[status(thm)],[t33065]) ).
cnf(t28652,plain,
true = ifeq(true,true,cong(sk23,X1,sk23,X2),true),
inference(cp,[status(thm)],[t336,t28651]) ).
cnf(t33085,plain,
true = cong(sk23,X1,sk23,X2),
inference(step,[status(thm)],[t28652,t256]) ).
cnf(t28757,plain,
cong(sk23,X1,sk23,X2) = true,
inference(orient,[status(thm)],[t33085]) ).
cnf(t28762,plain,
true = ifeq(true,true,cong(sk23,X1,X2,sk23),true),
inference(cp,[status(thm)],[t268,t28757]) ).
cnf(t33115,plain,
true = cong(sk23,X1,X2,sk23),
inference(step,[status(thm)],[t28762,t256]) ).
cnf(t28928,plain,
cong(sk23,X1,X2,sk23) = true,
inference(orient,[status(thm)],[t33115]) ).
cnf(t28933,plain,
true = ifeq(true,true,cong(X1,sk23,sk23,X2),true),
inference(cp,[status(thm)],[t266,t28928]) ).
cnf(t33127,plain,
true = cong(X1,sk23,sk23,X2),
inference(step,[status(thm)],[t28933,t256]) ).
cnf(t29066,plain,
cong(X1,sk23,sk23,X2) = true,
inference(orient,[status(thm)],[t33127]) ).
cnf(t29070,plain,
true = ifeq(true,true,cong(X1,sk23,X2,sk23),true),
inference(cp,[status(thm)],[t268,t29066]) ).
cnf(t33134,plain,
true = cong(X1,sk23,X2,sk23),
inference(step,[status(thm)],[t29070,t256]) ).
cnf(t29204,plain,
cong(X1,sk23,X2,sk23) = true,
inference(orient,[status(thm)],[t33134]) ).
cnf(t30351,plain,
true = ifeq(true,true,midp(X1,sk23,sk23),true),
inference(cp,[status(thm)],[t30342,t29204]) ).
cnf(t33242,plain,
true = midp(X1,sk23,sk23),
inference(step,[status(thm)],[t30351,t256]) ).
cnf(t30372,plain,
midp(X1,sk23,sk23) = true,
inference(orient,[status(thm)],[t33242]) ).
cnf(t30373,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t28583,t30372]) ).
cnf(t33254,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t30373,t256]) ).
cnf(t30442,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t33254]) ).
cnf(t33271,plain,
ifeq(true,true,cong(X1,X2,X1,X3),true) = true,
inference(step,[status(thm)],[t336,t30442]) ).
cnf(t33272,plain,
cong(X1,X2,X1,X3) = true,
inference(step,[status(thm)],[t33271,t256]) ).
cnf(t30451,plain,
cong(X1,X2,X1,X3) = true,
inference(rw,[status(thm)],[t33272]) ).
cnf(t30692,plain,
cong(X1,X2,X1,X3) = true,
inference(orient,[status(thm)],[t30451]) ).
cnf(t30696,plain,
true = ifeq(true,true,cong(X1,X2,X3,X1),true),
inference(cp,[status(thm)],[t268,t30692]) ).
cnf(t33305,plain,
true = cong(X1,X2,X3,X1),
inference(step,[status(thm)],[t30696,t256]) ).
cnf(t30757,plain,
cong(X1,X2,X3,X1) = true,
inference(orient,[status(thm)],[t33305]) ).
cnf(t30761,plain,
true = ifeq(true,true,cong(X1,X2,X2,X3),true),
inference(cp,[status(thm)],[t266,t30757]) ).
cnf(t33313,plain,
true = cong(X1,X2,X2,X3),
inference(step,[status(thm)],[t30761,t256]) ).
cnf(t30798,plain,
cong(X1,X2,X2,X3) = true,
inference(orient,[status(thm)],[t33313]) ).
cnf(t30802,plain,
true = ifeq(true,true,cong(X1,X2,X3,X2),true),
inference(cp,[status(thm)],[t268,t30798]) ).
cnf(t33315,plain,
true = cong(X1,X2,X3,X2),
inference(step,[status(thm)],[t30802,t256]) ).
cnf(t30822,plain,
cong(X1,X2,X3,X2) = true,
inference(orient,[status(thm)],[t33315]) ).
cnf(t33316,plain,
ifeq(true,true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(step,[status(thm)],[t271,t30822]) ).
cnf(t33317,plain,
ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t33316,t256]) ).
cnf(t33318,plain,
ifeq(true,true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t33317,t30822]) ).
cnf(t33319,plain,
perp(X1,X3,X2,X4) = true,
inference(step,[status(thm)],[t33318,t256]) ).
cnf(t30834,plain,
perp(X1,X3,X2,X4) = true,
inference(rw,[status(thm)],[t33319]) ).
cnf(t30835,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t30834]) ).
cnf(c121,plain,
~ perp(sk26,sk27,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk26,sk27,sk20,sk24) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t30835]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO633+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 12:36:56 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 208.88/26.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 208.88/26.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------