%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP105-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 01:30:54 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.29s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 51 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 28 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 118 !; 0 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
tcf(c_52,negated_conjecture,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))),X1) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(inverse(double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X0))))),inverse(X3))))),X2) = X3,
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] : double_divide(inverse(double_divide(X0,inverse(X0))),inverse(X1)) = X1,
inference(superposition,[status(thm)],[c_53,c_114]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0,inverse(X0))),X1),inverse(X2))),X1) = X2,
inference(superposition,[status(thm)],[c_118,c_53]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] : double_divide(inverse(double_divide(X0,inverse(X1))),inverse(X0)) = X1,
inference(superposition,[status(thm)],[c_118,c_114]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : double_divide(inverse(inverse(double_divide(X0,inverse(X0)))),inverse(X1)) = X1,
inference(superposition,[status(thm)],[c_118,c_118]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(inverse(double_divide(X1,inverse(X1))))) = X0,
inference(superposition,[status(thm)],[c_118,c_146]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,inverse(double_divide(inverse(double_divide(X1,inverse(X0))),inverse(X2))))),inverse(X1)) = X2,
inference(superposition,[status(thm)],[c_146,c_53]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0,inverse(X1))),X2),inverse(X1))),X2) = X0,
inference(superposition,[status(thm)],[c_146,c_53]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(X0,inverse(X0)))),X1),inverse(X2))),X1) = X2,
inference(superposition,[status(thm)],[c_148,c_53]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,inverse(inverse(double_divide(X1,inverse(X1))))),inverse(double_divide(X0,inverse(X2)))) = X2,
inference(superposition,[status(thm)],[c_180,c_53]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(X0))) = double_divide(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_180,c_118]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(X0))) = inverse(double_divide(X1,inverse(X1))),
inference(superposition,[status(thm)],[c_180,c_148]) ).
tcf(c_246,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_243]) ).
tcf(c_475,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(inverse(X0),X1),inverse(X2))),X1) = inverse(double_divide(X2,inverse(X0))),
inference(superposition,[status(thm)],[c_146,c_183]) ).
tcf(c_490,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(double_divide(X1,inverse(X1))))) = X0,
inference(demodulation,[status(thm)],[c_143,c_475]) ).
tcf(c_491,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_246,c_490]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(inverse(double_divide(X1,inverse(X1)))))) = X0,
inference(demodulation,[status(thm)],[c_198,c_475]) ).
tcf(c_895,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_242,c_180]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(inverse(double_divide(X0,inverse(inverse(double_divide(X1,inverse(X1)))))),X2) = inverse(double_divide(double_divide(X3,X2),inverse(double_divide(X3,inverse(X0))))),
inference(superposition,[status(thm)],[c_242,c_114]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))) = double_divide(X2,X1),
inference(light_normalisation,[status(thm)],[c_904,c_533]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_53,c_917]) ).
tcf(c_1041,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(X1))) = double_divide(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_146,c_918]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i] : double_divide(X0,inverse(inverse(double_divide(X1,inverse(X1))))) = inverse(X0),
inference(superposition,[status(thm)],[c_918,c_533]) ).
tcf(c_1078,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),inverse(c3)) ) ),
inference(demodulation,[status(thm)],[c_491,c_1041]) ).
tcf(c_1081,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),double_divide(X1,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[c_895,c_1041]) ).
tcf(c_1085,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,inverse(X1))) = inverse(X0),
inference(superposition,[status(thm)],[c_1081,c_918]) ).
tcf(c_1086,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_1081,c_1085]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(double_divide(X0,inverse(X1)))) = X1,
inference(light_normalisation,[status(thm)],[c_234,c_1046]) ).
tcf(c_1166,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),double_divide(X1,inverse(X0))) = X1,
inference(light_normalisation,[status(thm)],[c_1165,c_1041]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_1086,c_1166]) ).
tcf(c_1182,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_918,c_1173]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_1173,c_918]) ).
tcf(c_1190,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(double_divide(a3,b3),inverse(c3)) ) ),
inference(demodulation,[status(thm)],[c_1078,c_1182]) ).
tcf(c_1215,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(double_divide(a3,b3),inverse(c3)),
inference(ground_joinability,[status(thm)],[c_1190,c_1182]) ).
tcf(c_1216,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(demodulation,[status(thm)],[c_1215,c_1041,c_1182]) ).
tcf(c_1218,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(X0),X1)) = double_divide(X0,inverse(X1)),
inference(superposition,[status(thm)],[c_1182,c_1041]) ).
tcf(c_1249,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,inverse(X1)),inverse(X2)) = inverse(double_divide(double_divide(X1,inverse(X0)),X2)),
inference(superposition,[status(thm)],[c_1041,c_1218]) ).
tcf(c_1250,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(X1)) = inverse(double_divide(X0,X1)),
inference(superposition,[status(thm)],[c_1086,c_1218]) ).
tcf(c_1251,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(inverse(X0),X1),inverse(X2)) = inverse(double_divide(double_divide(X0,inverse(X1)),X2)),
inference(superposition,[status(thm)],[c_1218,c_1218]) ).
tcf(c_1254,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(X1))) = double_divide(inverse(X0),X1),
inference(superposition,[status(thm)],[c_1218,c_1086]) ).
tcf(c_1686,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,double_divide(X1,double_divide(double_divide(inverse(X1),X0),X2)))) = X2,
inference(demodulation,[status(thm)],[c_182,c_1182,c_1218,c_1249,c_1250,c_1254]) ).
tcf(c_1698,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(inverse(X0),X1),X2) = inverse(double_divide(X1,double_divide(X0,X2))),
inference(superposition,[status(thm)],[c_1185,c_1686]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(inverse(X1),X2)) = inverse(double_divide(X2,double_divide(X1,X0))),
inference(superposition,[status(thm)],[c_1173,c_1686]) ).
tcf(c_2710,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,inverse(X1)),X2) = inverse(double_divide(X0,double_divide(X1,X2))),
inference(superposition,[status(thm)],[c_1182,c_1698]) ).
tcf(c_2720,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,double_divide(inverse(X1),X2))) = double_divide(double_divide(X1,X0),X2),
inference(superposition,[status(thm)],[c_1086,c_1698]) ).
tcf(c_2725,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(X2,X0)))) = double_divide(inverse(X2),X1),
inference(superposition,[status(thm)],[c_1698,c_1173]) ).
tcf(c_2737,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(double_divide(X0,double_divide(X1,X2)))) = double_divide(double_divide(X1,X2),X0),
inference(light_normalisation,[status(thm)],[c_2720,c_1700]) ).
tcf(c_2967,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(X0,X1),X2)),X0) = inverse(double_divide(X1,inverse(X2))),
inference(light_normalisation,[status(thm)],[c_475,c_1251,c_2710,c_2737]) ).
tcf(c_2968,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(double_divide(X0,X1),X2))) = double_divide(inverse(X1),X2),
inference(demodulation,[status(thm)],[c_2967,c_1182,c_1254]) ).
tcf(c_3191,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(X0),double_divide(X1,X2)) = double_divide(inverse(X1),double_divide(X2,X0)),
inference(superposition,[status(thm)],[c_2725,c_2968]) ).
tcf(c_3201,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(demodulation,[status(thm)],[c_1216,c_3191]) ).
tcf(c_3202,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_3201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP105-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 13:33:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 1.30/1.29 % SZS status Started for theBenchmark.p
% 1.30/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.29
% 1.30/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.30/1.29
% 1.30/1.29 % ------ iProver source info
% 1.30/1.29
% 1.30/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.30/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.30/1.29 % git: non_committed_changes: false
% 1.30/1.29
% 1.30/1.29 % ------ Parsing...% successful
% 1.30/1.29
% 1.30/1.29
% 1.30/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.30/1.29
% 1.30/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.30/1.29
% 1.30/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.30/1.29
% 1.30/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.30/1.29 % ------ Proving...
% 1.30/1.29 % ------ Problem Properties
% 1.30/1.29
% 1.30/1.29 %
% 1.30/1.29 % clauses 2
% 1.30/1.29 % conjectures 1
% 1.30/1.29 % EPR 0
% 1.30/1.29 % Horn 2
% 1.30/1.29 % unary 1
% 1.30/1.29 % binary 0
% 1.30/1.29 % lits 5
% 1.30/1.29 % lits eq 5
% 1.30/1.29 % fd_pure 0
% 1.30/1.29 % fd_pseudo 0
% 1.30/1.29 % fd_cond 0
% 1.30/1.29 % fd_pseudo_cond 0
% 1.30/1.29 % AC symbols 0
% 1.30/1.29
% 1.30/1.29 % ------ Schedule dynamic 5 is on
% 1.30/1.29
% 1.30/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.30/1.29
% 1.30/1.29
% 1.30/1.29 % ------
% 1.30/1.29 % Current options:
% 1.30/1.29 % ------
% 1.30/1.29
% 1.30/1.29
% 1.30/1.29 %
% 1.30/1.29
% 1.30/1.29 % ------ Proving...
% 1.30/1.29 %
% 1.30/1.29
% 1.30/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.29
% 1.30/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.30/1.30
% 1.30/1.30
%------------------------------------------------------------------------------