%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO637+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 : 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 120.47s 16.00s
% Output : Proof 120.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 20
% Syntax : Number of formulae : 218 ( 142 unt; 0 def)
% Number of atoms : 350 ( 138 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 219 ( 87 ~; 81 |; 31 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 728 ( 113 sgn 254 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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(t236,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t273,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t236]) ).
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(t109,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)],[t109]) ).
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(t228,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)],[t228]) ).
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(t189,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)],[t189]) ).
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(t125,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)],[t125]) ).
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(t176,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)],[t176]) ).
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(t157,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)],[t157]) ).
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(t181,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)],[t181]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f94,conjecture,
! [A,B,C,O,H,D,E] :
( ( perp(A,O,A,E)
& perp(C,O,C,E)
& coll(D,A,B)
& coll(D,O,H)
& midp(H,C,B)
& circle(O,A,B,C) )
=> cyclic(A,O,E,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL81109101) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,H,D,E] :
( ( perp(A,O,A,E)
& perp(C,O,C,E)
& coll(D,A,B)
& coll(D,O,H)
& midp(H,C,B)
& circle(O,A,B,C) )
=> cyclic(A,O,E,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,H,D,E] :
( ~ cyclic(A,O,E,D)
& perp(A,O,A,E)
& perp(C,O,C,E)
& coll(D,A,B)
& coll(D,O,H)
& midp(H,C,B)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk20,sk23,sk26,sk25)
& perp(sk20,sk23,sk20,sk26)
& perp(sk22,sk23,sk22,sk26)
& coll(sk25,sk20,sk21)
& 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])],[f94_nnf]) ).
cnf(c118,plain,
perp(sk20,sk23,sk20,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
perp(sk20,sk23,sk20,sk26) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h26,plain,
perp(sk20,sk26,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi118]) ).
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(h148,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi118,h26]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t60,plain,
eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h148]) ).
cnf(t1700,plain,
eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t60]) ).
cnf(t1709,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23),true),
inference(cp,[status(thm)],[t308,t1700]) ).
cnf(t41,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t41]) ).
cnf(t22485,plain,
true = eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23),
inference(step,[status(thm)],[t1709,t256]) ).
cnf(t9662,plain,
eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23) = true,
inference(orient,[status(thm)],[t22485]) ).
cnf(t9665,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t9662]) ).
cnf(t22486,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t9665,t256]) ).
cnf(t9688,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t22486]) ).
cnf(t9705,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,t9688]) ).
cnf(t23398,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)],[t9705,t256]) ).
cnf(t23399,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t23398,t9688]) ).
cnf(t23400,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t23399,t256]) ).
cnf(t18968,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t23400]) ).
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(t167,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)],[t167]) ).
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(t162,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)],[t162]) ).
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(t105,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)],[t105]) ).
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(t106,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)],[t106]) ).
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(t110,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)],[t110]) ).
cnf(t9689,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t9688]) ).
cnf(t22487,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t9689,t256]) ).
cnf(t9714,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t22487]) ).
cnf(t9716,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t9714]) ).
cnf(t22488,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t9716,t256]) ).
cnf(t9758,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t22488]) ).
cnf(t9761,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t9758]) ).
cnf(t22489,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t9761,t256]) ).
cnf(t9790,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t22489]) ).
cnf(t9793,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t9790]) ).
cnf(t22490,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t9793,t256]) ).
cnf(t22491,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t22490,t9790]) ).
cnf(t22492,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t22491,t256]) ).
cnf(t9824,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t22492]) ).
cnf(t22503,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t9824]) ).
cnf(t22504,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t22503,t256]) ).
cnf(t9831,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t22504]) ).
cnf(t19855,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t9831]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(c114,plain,
midp(sk24,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
midp(sk24,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h6,plain,
cong(sk24,sk22,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi114]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h9,plain,
midp(sk24,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi114]) ).
cnf(h50,plain,
cong(sk24,sk21,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi68,h9]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(cong(X0,X1,X2,X3),true,ifeq(cong(X2,X3,X4,X5),true,cong(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t21,plain,
cong(sk24,sk21,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi24,h50,h6]) ).
cnf(t1106,plain,
cong(sk24,sk21,sk24,sk21) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t19858,plain,
true = ifeq(true,true,midp(sk24,sk21,sk21),true),
inference(cp,[status(thm)],[t19855,t1106]) ).
cnf(t23556,plain,
true = midp(sk24,sk21,sk21),
inference(step,[status(thm)],[t19858,t256]) ).
cnf(t19866,plain,
midp(sk24,sk21,sk21) = true,
inference(orient,[status(thm)],[t23556]) ).
cnf(t19873,plain,
true = ifeq(true,true,midp(sk24,X1,X1),true),
inference(cp,[status(thm)],[t18968,t19866]) ).
cnf(t23564,plain,
true = midp(sk24,X1,X1),
inference(step,[status(thm)],[t19873,t256]) ).
cnf(t20044,plain,
midp(sk24,X1,X1) = true,
inference(orient,[status(thm)],[t23564]) ).
cnf(t20053,plain,
true = ifeq(true,true,cong(sk24,X1,sk24,X1),true),
inference(cp,[status(thm)],[t336,t20044]) ).
cnf(t23573,plain,
true = cong(sk24,X1,sk24,X1),
inference(step,[status(thm)],[t20053,t256]) ).
cnf(t20205,plain,
cong(sk24,X1,sk24,X1) = true,
inference(orient,[status(thm)],[t23573]) ).
cnf(t20220,plain,
true = ifeq(true,true,ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t20205]) ).
cnf(t23591,plain,
true = ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t20220,t256]) ).
cnf(t23592,plain,
true = ifeq(true,true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t23591,t20205]) ).
cnf(t23593,plain,
true = perp(sk24,sk24,X2,X1),
inference(step,[status(thm)],[t23592,t256]) ).
cnf(t20535,plain,
perp(sk24,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t23593]) ).
cnf(t20536,plain,
true = ifeq(true,true,perp(X1,X2,sk24,sk24),true),
inference(cp,[status(thm)],[t292,t20535]) ).
cnf(t23612,plain,
true = perp(X1,X2,sk24,sk24),
inference(step,[status(thm)],[t20536,t256]) ).
cnf(t20806,plain,
perp(X1,X2,sk24,sk24) = true,
inference(orient,[status(thm)],[t23612]) ).
cnf(t20813,plain,
true = ifeq(true,true,ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t20806]) ).
cnf(t23620,plain,
true = ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20813,t256]) ).
cnf(t23621,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t23620,t20535]) ).
cnf(t23622,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t23621,t256]) ).
cnf(t21010,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t23622]) ).
cnf(t23634,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,t21010]) ).
cnf(t23635,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)],[t23634,t256]) ).
cnf(t23636,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t23635,t21010]) ).
cnf(t23637,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t23636,t256]) ).
cnf(t21017,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t23637]) ).
cnf(t21339,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t21017]) ).
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(t117,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)],[t117]) ).
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(t118,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)],[t118]) ).
cnf(t20210,plain,
true = ifeq(true,true,cong(sk24,X1,X1,sk24),true),
inference(cp,[status(thm)],[t268,t20205]) ).
cnf(t23590,plain,
true = cong(sk24,X1,X1,sk24),
inference(step,[status(thm)],[t20210,t256]) ).
cnf(t20503,plain,
cong(sk24,X1,X1,sk24) = true,
inference(orient,[status(thm)],[t23590]) ).
cnf(t20507,plain,
true = ifeq(true,true,cong(X1,sk24,sk24,X1),true),
inference(cp,[status(thm)],[t266,t20503]) ).
cnf(t23611,plain,
true = cong(X1,sk24,sk24,X1),
inference(step,[status(thm)],[t20507,t256]) ).
cnf(t20778,plain,
cong(X1,sk24,sk24,X1) = true,
inference(orient,[status(thm)],[t23611]) ).
cnf(t20782,plain,
true = ifeq(true,true,cong(X1,sk24,X1,sk24),true),
inference(cp,[status(thm)],[t268,t20778]) ).
cnf(t23617,plain,
true = cong(X1,sk24,X1,sk24),
inference(step,[status(thm)],[t20782,t256]) ).
cnf(t20934,plain,
cong(X1,sk24,X1,sk24) = true,
inference(orient,[status(thm)],[t23617]) ).
cnf(t20935,plain,
true = ifeq(true,true,midp(X1,sk24,sk24),true),
inference(cp,[status(thm)],[t19855,t20934]) ).
cnf(t23618,plain,
true = midp(X1,sk24,sk24),
inference(step,[status(thm)],[t20935,t256]) ).
cnf(t20966,plain,
midp(X1,sk24,sk24) = true,
inference(orient,[status(thm)],[t23618]) ).
cnf(t20967,plain,
true = ifeq(true,true,midp(X1,X2,X2),true),
inference(cp,[status(thm)],[t18968,t20966]) ).
cnf(t23619,plain,
true = midp(X1,X2,X2),
inference(step,[status(thm)],[t20967,t256]) ).
cnf(t20985,plain,
midp(X1,X2,X2) = true,
inference(orient,[status(thm)],[t23619]) ).
cnf(t21340,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t21339,t20985]) ).
cnf(t23681,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t21340,t256]) ).
cnf(t21347,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t23681]) ).
cnf(t23722,plain,
ifeq(true,true,cong(X1,X2,X1,X3),true) = true,
inference(step,[status(thm)],[t336,t21347]) ).
cnf(t23723,plain,
cong(X1,X2,X1,X3) = true,
inference(step,[status(thm)],[t23722,t256]) ).
cnf(t21368,plain,
cong(X1,X2,X1,X3) = true,
inference(rw,[status(thm)],[t23723]) ).
cnf(t21871,plain,
cong(X1,X2,X1,X3) = true,
inference(orient,[status(thm)],[t21368]) ).
cnf(t23739,plain,
ifeq(true,true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t273,t21871]) ).
cnf(t23740,plain,
ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true) = true,
inference(step,[status(thm)],[t23739,t256]) ).
cnf(t23741,plain,
ifeq(true,true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true) = true,
inference(step,[status(thm)],[t23740,t21871]) ).
cnf(t23742,plain,
ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true) = true,
inference(step,[status(thm)],[t23741,t256]) ).
cnf(t23743,plain,
ifeq(true,true,cyclic(X2,X3,X4,X5),true) = true,
inference(step,[status(thm)],[t23742,t21871]) ).
cnf(t23744,plain,
cyclic(X2,X3,X4,X5) = true,
inference(step,[status(thm)],[t23743,t256]) ).
cnf(t21897,plain,
cyclic(X2,X3,X4,X5) = true,
inference(rw,[status(thm)],[t23744]) ).
cnf(t22226,plain,
cyclic(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t21897]) ).
cnf(c119,plain,
~ cyclic(sk20,sk23,sk26,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk20,sk23,sk26,sk25) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t22226]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO637+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:37:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 120.47/16.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 120.47/16.00 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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