%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO604+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 01:18:16 PM UTC 2026
% Result : Theorem 223.64s 28.77s
% Output : Proof 223.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 101
% Number of leaves : 24
% Syntax : Number of formulae : 326 ( 234 unt; 0 def)
% Number of atoms : 478 ( 227 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 254 ( 102 ~; 96 |; 32 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 881 ( 154 sgn 302 !; 7 ?)
% 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/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(t174,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)],[t174]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/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(t100,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)],[t100]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/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(t101,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)],[t101]) ).
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(t97,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)],[t97]) ).
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(t227,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)],[t227]) ).
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(t187,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)],[t187]) ).
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(t108,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)],[t108]) ).
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(t153,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)],[t153]) ).
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(t179,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)],[t179]) ).
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(t154,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)],[t154]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/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(t152,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)],[t152]) ).
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]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G] :
( ( midp(G,C,B)
& midp(F,A,E)
& coll(E,C,D)
& perp(B,C,A,E)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(D,G,D,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618066) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( midp(G,C,B)
& midp(F,A,E)
& coll(E,C,D)
& perp(B,C,A,E)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(D,G,D,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G] :
( ~ perp(D,G,D,F)
& midp(G,C,B)
& midp(F,A,E)
& coll(E,C,D)
& perp(B,C,A,E)
& coll(D,A,B)
& perp(D,C,A,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk23,sk26,sk23,sk25)
& midp(sk26,sk22,sk21)
& midp(sk25,sk20,sk24)
& coll(sk24,sk22,sk23)
& perp(sk21,sk22,sk20,sk24)
& coll(sk23,sk20,sk21)
& perp(sk23,sk22,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f94_nnf]) ).
cnf(c116,plain,
coll(sk24,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk24,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h8,plain,
coll(sk22,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi116]) ).
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]) ).
cnf(h54,plain,
coll(sk23,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c113,plain,
perp(sk23,sk22,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk23,sk22,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk20,sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
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(h38,plain,
para(sk23,sk22,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi113,h0]) ).
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(h393,plain,
eqangle(sk23,sk22,V0,V1,sk23,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h38]) ).
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(t23,plain,
cyclic(sk22,sk22,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h393,h54]) ).
cnf(t2853,plain,
cyclic(sk22,sk22,sk23,sk23) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t2856,plain,
true = ifeq(true,true,eqangle(sk23,sk22,sk23,sk22,sk23,sk22,sk23,sk22),true),
inference(cp,[status(thm)],[t359,t2853]) ).
cnf(t31,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t31]) ).
cnf(t34671,plain,
true = eqangle(sk23,sk22,sk23,sk22,sk23,sk22,sk23,sk22),
inference(step,[status(thm)],[t2856,t256]) ).
cnf(t7079,plain,
eqangle(sk23,sk22,sk23,sk22,sk23,sk22,sk23,sk22) = true,
inference(orient,[status(thm)],[t34671]) ).
cnf(t7080,plain,
true = ifeq(true,true,para(sk23,sk22,sk23,sk22),true),
inference(cp,[status(thm)],[t314,t7079]) ).
cnf(t34672,plain,
true = para(sk23,sk22,sk23,sk22),
inference(step,[status(thm)],[t7080,t256]) ).
cnf(t7094,plain,
para(sk23,sk22,sk23,sk22) = true,
inference(orient,[status(thm)],[t34672]) ).
cnf(t7098,plain,
true = ifeq(true,true,eqangle(sk23,sk22,X1,X2,sk23,sk22,X1,X2),true),
inference(cp,[status(thm)],[t346,t7094]) ).
cnf(t35075,plain,
true = eqangle(sk23,sk22,X1,X2,sk23,sk22,X1,X2),
inference(step,[status(thm)],[t7098,t256]) ).
cnf(t13091,plain,
eqangle(sk23,sk22,X1,X2,sk23,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t35075]) ).
cnf(t13096,plain,
true = ifeq(true,true,eqangle(X1,X2,sk23,sk22,X1,X2,sk23,sk22),true),
inference(cp,[status(thm)],[t308,t13091]) ).
cnf(t35568,plain,
true = eqangle(X1,X2,sk23,sk22,X1,X2,sk23,sk22),
inference(step,[status(thm)],[t13096,t256]) ).
cnf(t17839,plain,
eqangle(X1,X2,sk23,sk22,X1,X2,sk23,sk22) = true,
inference(orient,[status(thm)],[t35568]) ).
cnf(t17841,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t17839]) ).
cnf(t35569,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t17841,t256]) ).
cnf(t17863,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t35569]) ).
cnf(t17880,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,t17863]) ).
cnf(t36980,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)],[t17880,t256]) ).
cnf(t36981,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t36980,t17863]) ).
cnf(t36982,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t36981,t256]) ).
cnf(t30513,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t36982]) ).
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(t165,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)],[t165]) ).
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(t253,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)],[t253]) ).
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(t103,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t362,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t103]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/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(t104,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t104]) ).
cnf(c114,plain,
coll(sk23,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
coll(sk23,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h2,plain,
coll(sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi114,hi114]) ).
cnf(h36,plain,
coll(sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(t22,plain,
cyclic(sk22,sk21,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h393,h36]) ).
cnf(t2889,plain,
cyclic(sk22,sk21,sk23,sk23) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t2892,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk23,sk23),true),
inference(cp,[status(thm)],[t360,t2889]) ).
cnf(t34533,plain,
true = cyclic(sk21,sk22,sk23,sk23),
inference(step,[status(thm)],[t2892,t256]) ).
cnf(t4618,plain,
cyclic(sk21,sk22,sk23,sk23) = true,
inference(orient,[status(thm)],[t34533]) ).
cnf(t4619,plain,
true = ifeq(true,true,cyclic(sk21,sk23,sk22,sk23),true),
inference(cp,[status(thm)],[t362,t4618]) ).
cnf(t34566,plain,
true = cyclic(sk21,sk23,sk22,sk23),
inference(step,[status(thm)],[t4619,t256]) ).
cnf(t5250,plain,
cyclic(sk21,sk23,sk22,sk23) = true,
inference(orient,[status(thm)],[t34566]) ).
cnf(t5255,plain,
true = ifeq(true,true,eqangle(sk22,sk21,sk22,sk23,sk23,sk21,sk23,sk23),true),
inference(cp,[status(thm)],[t359,t5250]) ).
cnf(t34886,plain,
true = eqangle(sk22,sk21,sk22,sk23,sk23,sk21,sk23,sk23),
inference(step,[status(thm)],[t5255,t256]) ).
cnf(t11283,plain,
eqangle(sk22,sk21,sk22,sk23,sk23,sk21,sk23,sk23) = true,
inference(orient,[status(thm)],[t34886]) ).
cnf(t11299,plain,
true = ifeq(cyclic(sk21,sk23,sk22,sk21),true,ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),true),
inference(cp,[status(thm)],[t357,t11283]) ).
cnf(c115,plain,
perp(sk21,sk22,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
perp(sk21,sk22,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h5,plain,
perp(sk20,sk24,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi115]) ).
cnf(h47,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi115,h5]) ).
cnf(h409,plain,
eqangle(sk21,sk22,V0,V1,sk21,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h47]) ).
cnf(t24,plain,
cyclic(sk22,sk23,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h409,h2]) ).
cnf(t2965,plain,
cyclic(sk22,sk23,sk21,sk21) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(t2966,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk23,sk21),true),
inference(cp,[status(thm)],[t362,t2965]) ).
cnf(t34540,plain,
true = cyclic(sk22,sk21,sk23,sk21),
inference(step,[status(thm)],[t2966,t256]) ).
cnf(t4740,plain,
cyclic(sk22,sk21,sk23,sk21) = true,
inference(orient,[status(thm)],[t34540]) ).
cnf(t4743,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk23,sk21),true),
inference(cp,[status(thm)],[t360,t4740]) ).
cnf(t34577,plain,
true = cyclic(sk21,sk22,sk23,sk21),
inference(step,[status(thm)],[t4743,t256]) ).
cnf(t5447,plain,
cyclic(sk21,sk22,sk23,sk21) = true,
inference(orient,[status(thm)],[t34577]) ).
cnf(t5450,plain,
true = ifeq(true,true,cyclic(sk21,sk23,sk22,sk21),true),
inference(cp,[status(thm)],[t362,t5447]) ).
cnf(t34617,plain,
true = cyclic(sk21,sk23,sk22,sk21),
inference(step,[status(thm)],[t5450,t256]) ).
cnf(t6148,plain,
cyclic(sk21,sk23,sk22,sk21) = true,
inference(orient,[status(thm)],[t34617]) ).
cnf(t34887,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),true),
inference(step,[status(thm)],[t11299,t6148]) ).
cnf(t34888,plain,
true = ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),
inference(step,[status(thm)],[t34887,t256]) ).
cnf(t34889,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),true),
inference(step,[status(thm)],[t34888,t5250]) ).
cnf(t34890,plain,
true = ifeq(cyclic(sk21,sk23,sk22,sk23),true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),
inference(step,[status(thm)],[t34889,t256]) ).
cnf(t34891,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),true),
inference(step,[status(thm)],[t34890,t5250]) ).
cnf(t34892,plain,
true = ifeq(true,true,cong(sk21,sk23,sk21,sk23),true),
inference(step,[status(thm)],[t34891,t256]) ).
cnf(t34893,plain,
true = cong(sk21,sk23,sk21,sk23),
inference(step,[status(thm)],[t34892,t256]) ).
cnf(t11300,plain,
cong(sk21,sk23,sk21,sk23) = true,
inference(orient,[status(thm)],[t34893]) ).
cnf(t11312,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk23,sk23),true,midp(sk21,sk23,sk23),true),true),
inference(cp,[status(thm)],[t272,t11300]) ).
cnf(t34894,plain,
true = ifeq(coll(sk21,sk23,sk23),true,midp(sk21,sk23,sk23),true),
inference(step,[status(thm)],[t11312,t256]) ).
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(t98,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)],[t98]) ).
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(t105,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t350,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t105]) ).
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(t106,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t347,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t106]) ).
cnf(t4621,plain,
true = ifeq(true,true,eqangle(sk23,sk21,sk23,sk22,sk23,sk21,sk23,sk22),true),
inference(cp,[status(thm)],[t359,t4618]) ).
cnf(t34803,plain,
true = eqangle(sk23,sk21,sk23,sk22,sk23,sk21,sk23,sk22),
inference(step,[status(thm)],[t4621,t256]) ).
cnf(t9424,plain,
eqangle(sk23,sk21,sk23,sk22,sk23,sk21,sk23,sk22) = true,
inference(orient,[status(thm)],[t34803]) ).
cnf(t9425,plain,
true = ifeq(true,true,para(sk23,sk21,sk23,sk21),true),
inference(cp,[status(thm)],[t314,t9424]) ).
cnf(t34804,plain,
true = para(sk23,sk21,sk23,sk21),
inference(step,[status(thm)],[t9425,t256]) ).
cnf(t9437,plain,
para(sk23,sk21,sk23,sk21) = true,
inference(orient,[status(thm)],[t34804]) ).
cnf(t9439,plain,
true = ifeq(true,true,para(sk23,sk21,sk21,sk23),true),
inference(cp,[status(thm)],[t350,t9437]) ).
cnf(t34808,plain,
true = para(sk23,sk21,sk21,sk23),
inference(step,[status(thm)],[t9439,t256]) ).
cnf(t9554,plain,
para(sk23,sk21,sk21,sk23) = true,
inference(orient,[status(thm)],[t34808]) ).
cnf(t9555,plain,
true = ifeq(true,true,para(sk21,sk23,sk23,sk21),true),
inference(cp,[status(thm)],[t347,t9554]) ).
cnf(t34809,plain,
true = para(sk21,sk23,sk23,sk21),
inference(step,[status(thm)],[t9555,t256]) ).
cnf(t9578,plain,
para(sk21,sk23,sk23,sk21) = true,
inference(orient,[status(thm)],[t34809]) ).
cnf(t9579,plain,
true = ifeq(true,true,para(sk21,sk23,sk21,sk23),true),
inference(cp,[status(thm)],[t350,t9578]) ).
cnf(t34810,plain,
true = para(sk21,sk23,sk21,sk23),
inference(step,[status(thm)],[t9579,t256]) ).
cnf(t9601,plain,
para(sk21,sk23,sk21,sk23) = true,
inference(orient,[status(thm)],[t34810]) ).
cnf(t9602,plain,
true = ifeq(true,true,coll(sk21,sk23,sk23),true),
inference(cp,[status(thm)],[t353,t9601]) ).
cnf(t34811,plain,
true = coll(sk21,sk23,sk23),
inference(step,[status(thm)],[t9602,t256]) ).
cnf(t9625,plain,
coll(sk21,sk23,sk23) = true,
inference(orient,[status(thm)],[t34811]) ).
cnf(t34895,plain,
true = ifeq(true,true,midp(sk21,sk23,sk23),true),
inference(step,[status(thm)],[t34894,t9625]) ).
cnf(t34896,plain,
true = midp(sk21,sk23,sk23),
inference(step,[status(thm)],[t34895,t256]) ).
cnf(t11341,plain,
midp(sk21,sk23,sk23) = true,
inference(orient,[status(thm)],[t34896]) ).
cnf(t30514,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t30513,t11341]) ).
cnf(t36983,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t30514,t256]) ).
cnf(t30519,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t36983]) ).
cnf(t30520,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t336,t30519]) ).
cnf(t36986,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t30520,t256]) ).
cnf(t30579,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t36986]) ).
cnf(t30594,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t30579]) ).
cnf(t36990,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t30594,t256]) ).
cnf(t36991,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t36990,t30579]) ).
cnf(t36992,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t36991,t256]) ).
cnf(t30713,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t36992]) ).
cnf(t30714,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t292,t30713]) ).
cnf(t37002,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t30714,t256]) ).
cnf(t30885,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t37002]) ).
cnf(t30892,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t30885]) ).
cnf(t37009,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t30892,t256]) ).
cnf(t37010,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t37009,t30713]) ).
cnf(t37011,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t37010,t256]) ).
cnf(t31060,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t37011]) ).
cnf(t37023,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,t31060]) ).
cnf(t37024,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)],[t37023,t256]) ).
cnf(t37025,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t37024,t31060]) ).
cnf(t37026,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t37025,t256]) ).
cnf(t31067,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t37026]) ).
cnf(t32166,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t31067]) ).
cnf(t164,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)],[t164]) ).
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(t70,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)],[t70]) ).
cnf(t71,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)],[t71]) ).
cnf(t17864,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t17863]) ).
cnf(t35570,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t17864,t256]) ).
cnf(t17889,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t35570]) ).
cnf(t17891,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t17889]) ).
cnf(t35571,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t17891,t256]) ).
cnf(t17932,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t35571]) ).
cnf(t17935,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t17932]) ).
cnf(t35572,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t17935,t256]) ).
cnf(t17964,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t35572]) ).
cnf(t17967,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t17964]) ).
cnf(t35573,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t17967,t256]) ).
cnf(t35574,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t35573,t17964]) ).
cnf(t35575,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t35574,t256]) ).
cnf(t17998,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t35575]) ).
cnf(t35586,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t17998]) ).
cnf(t35587,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t35586,t256]) ).
cnf(t18005,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t35587]) ).
cnf(t34166,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t18005]) ).
cnf(c118,plain,
midp(sk26,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t14,plain,
midp(sk26,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(t2052,plain,
midp(sk26,sk22,sk21) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t32188,plain,
true = ifeq(true,true,midp(sk26,X1,X2),true),
inference(cp,[status(thm)],[t32166,t2052]) ).
cnf(t37171,plain,
true = midp(sk26,X1,X2),
inference(step,[status(thm)],[t32188,t256]) ).
cnf(t32229,plain,
midp(sk26,X1,X2) = true,
inference(orient,[status(thm)],[t37171]) ).
cnf(t32230,plain,
true = ifeq(true,true,cong(sk26,X1,sk26,X2),true),
inference(cp,[status(thm)],[t336,t32229]) ).
cnf(t37176,plain,
true = cong(sk26,X1,sk26,X2),
inference(step,[status(thm)],[t32230,t256]) ).
cnf(t32341,plain,
cong(sk26,X1,sk26,X2) = true,
inference(orient,[status(thm)],[t37176]) ).
cnf(t32343,plain,
true = ifeq(true,true,cong(sk26,X1,X2,sk26),true),
inference(cp,[status(thm)],[t268,t32341]) ).
cnf(t37197,plain,
true = cong(sk26,X1,X2,sk26),
inference(step,[status(thm)],[t32343,t256]) ).
cnf(t32527,plain,
cong(sk26,X1,X2,sk26) = true,
inference(orient,[status(thm)],[t37197]) ).
cnf(t32529,plain,
true = ifeq(true,true,cong(X1,sk26,sk26,X2),true),
inference(cp,[status(thm)],[t266,t32527]) ).
cnf(t37209,plain,
true = cong(X1,sk26,sk26,X2),
inference(step,[status(thm)],[t32529,t256]) ).
cnf(t32670,plain,
cong(X1,sk26,sk26,X2) = true,
inference(orient,[status(thm)],[t37209]) ).
cnf(t32672,plain,
true = ifeq(true,true,cong(X1,sk26,X2,sk26),true),
inference(cp,[status(thm)],[t268,t32670]) ).
cnf(t37215,plain,
true = cong(X1,sk26,X2,sk26),
inference(step,[status(thm)],[t32672,t256]) ).
cnf(t32806,plain,
cong(X1,sk26,X2,sk26) = true,
inference(orient,[status(thm)],[t37215]) ).
cnf(t34177,plain,
true = ifeq(true,true,midp(X1,sk26,sk26),true),
inference(cp,[status(thm)],[t34166,t32806]) ).
cnf(t37341,plain,
true = midp(X1,sk26,sk26),
inference(step,[status(thm)],[t34177,t256]) ).
cnf(t34187,plain,
midp(X1,sk26,sk26) = true,
inference(orient,[status(thm)],[t37341]) ).
cnf(t34188,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t32166,t34187]) ).
cnf(t37348,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t34188,t256]) ).
cnf(t34246,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t37348]) ).
cnf(t37357,plain,
ifeq(true,true,cong(X1,X2,X1,X3),true) = true,
inference(step,[status(thm)],[t336,t34246]) ).
cnf(t37358,plain,
cong(X1,X2,X1,X3) = true,
inference(step,[status(thm)],[t37357,t256]) ).
cnf(t34251,plain,
cong(X1,X2,X1,X3) = true,
inference(rw,[status(thm)],[t37358]) ).
cnf(t34359,plain,
cong(X1,X2,X1,X3) = true,
inference(orient,[status(thm)],[t34251]) ).
cnf(t34361,plain,
true = ifeq(true,true,cong(X1,X2,X3,X1),true),
inference(cp,[status(thm)],[t268,t34359]) ).
cnf(t37388,plain,
true = cong(X1,X2,X3,X1),
inference(step,[status(thm)],[t34361,t256]) ).
cnf(t34390,plain,
cong(X1,X2,X3,X1) = true,
inference(orient,[status(thm)],[t37388]) ).
cnf(t34392,plain,
true = ifeq(true,true,cong(X1,X2,X2,X3),true),
inference(cp,[status(thm)],[t266,t34390]) ).
cnf(t37396,plain,
true = cong(X1,X2,X2,X3),
inference(step,[status(thm)],[t34392,t256]) ).
cnf(t34422,plain,
cong(X1,X2,X2,X3) = true,
inference(orient,[status(thm)],[t37396]) ).
cnf(t34424,plain,
true = ifeq(true,true,cong(X1,X2,X3,X2),true),
inference(cp,[status(thm)],[t268,t34422]) ).
cnf(t37398,plain,
true = cong(X1,X2,X3,X2),
inference(step,[status(thm)],[t34424,t256]) ).
cnf(t34459,plain,
cong(X1,X2,X3,X2) = true,
inference(orient,[status(thm)],[t37398]) ).
cnf(t37399,plain,
ifeq(true,true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(step,[status(thm)],[t271,t34459]) ).
cnf(t37400,plain,
ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t37399,t256]) ).
cnf(t37401,plain,
ifeq(true,true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t37400,t34459]) ).
cnf(t37402,plain,
perp(X1,X3,X2,X4) = true,
inference(step,[status(thm)],[t37401,t256]) ).
cnf(t34474,plain,
perp(X1,X3,X2,X4) = true,
inference(rw,[status(thm)],[t37402]) ).
cnf(t34487,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t34474]) ).
cnf(c119,plain,
~ perp(sk23,sk26,sk23,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk23,sk26,sk23,sk25) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t34487]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO604+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:37:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 223.64/28.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 223.64/28.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------