TSTP Solution File: GRP194+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:12:57 EDT 2022
% Result : Theorem 189.39s 183.62s
% Output : Proof 189.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : leancop_casc.sh %s %d
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 12:15:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 189.39/183.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 189.39/183.63 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 189.39/183.63
% 189.39/183.63 %-----------------------------------------------------
% 189.39/183.63 fof(homomorphism2, axiom, ! [_36670, _36673] : (group_member(_36670, f) & group_member(_36673, f) => multiply(h, phi(_36670), phi(_36673)) = phi(multiply(f, _36670, _36673))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', homomorphism2)).
% 189.39/183.63 fof(prove_left_zero_h, conjecture, left_zero(h, phi(f_left_zero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prove_left_zero_h)).
% 189.39/183.63 fof(surjective, axiom, ! [_36979] : (group_member(_36979, h) => ? [_36997] : (group_member(_36997, f) & phi(_36997) = _36979)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', surjective)).
% 189.39/183.63 fof(homomorphism1, axiom, ! [_37227] : (group_member(_37227, f) => group_member(phi(_37227), h)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', homomorphism1)).
% 189.39/183.63 fof(left_zero, axiom, ! [_37371, _37374] : (left_zero(_37371, _37374) <=> group_member(_37374, _37371) & ! [_37402] : (group_member(_37402, _37371) => multiply(_37371, _37374, _37402) = _37374)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', left_zero)).
% 189.39/183.63 fof(left_zero_for_f, hypothesis, left_zero(f, f_left_zero), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', left_zero_for_f)).
% 189.39/183.63
% 189.39/183.63 cnf(1, plain, [-(multiply(h, phi(_11628), phi(_11693)) = phi(multiply(f, _11628, _11693))), group_member(_11628, f), group_member(_11693, f)], clausify(homomorphism2)).
% 189.39/183.63 cnf(2, plain, [left_zero(h, phi(f_left_zero))], clausify(prove_left_zero_h)).
% 189.39/183.63 cnf(3, plain, [-(_6629 = _6740), _6629 = _6685, _6685 = _6740], theory(equality)).
% 189.39/183.63 cnf(4, plain, [group_member(_12254, h), -(group_member(1 ^ [_12254], f))], clausify(surjective)).
% 189.39/183.63 cnf(5, plain, [group_member(_12254, h), -(phi(1 ^ [_12254]) = _12254)], clausify(surjective)).
% 189.39/183.63 cnf(6, plain, [_9388 = _9437, -(phi(_9388) = phi(_9437))], theory(equality)).
% 189.39/183.63 cnf(7, plain, [-(left_zero(_7786, _7917)), left_zero(_7719, _7852), _7719 = _7786, _7852 = _7917], theory(equality)).
% 189.39/183.63 cnf(8, plain, [-(multiply(_8373, _8542, _8707) = multiply(_8458, _8625, _8788)), _8373 = _8458, _8542 = _8625, _8707 = _8788], theory(equality)).
% 189.39/183.63 cnf(9, plain, [group_member(_11356, f), -(group_member(phi(_11356), h))], clausify(homomorphism1)).
% 189.39/183.63 cnf(10, plain, [left_zero(_12665, _12731), -(group_member(_12731, _12665))], clausify(left_zero)).
% 189.39/183.63 cnf(11, plain, [-(_6197 = _6197)], theory(equality)).
% 189.39/183.63 cnf(12, plain, [-(left_zero(f, f_left_zero))], clausify(left_zero_for_f)).
% 189.39/183.63 cnf(13, plain, [_6350 = _6395, -(_6395 = _6350)], theory(equality)).
% 189.39/183.63 cnf(14, plain, [left_zero(_12665, _12731), group_member(_12914, _12665), -(multiply(_12665, _12731, _12914) = _12731)], clausify(left_zero)).
% 189.39/183.63 cnf(15, plain, [-(left_zero(_12665, _12731)), group_member(_12731, _12665), -(group_member(2 ^ [_12731, _12665], _12665))], clausify(left_zero)).
% 189.39/183.63 cnf(16, plain, [-(left_zero(_12665, _12731)), group_member(_12731, _12665), multiply(_12665, _12731, 2 ^ [_12731, _12665]) = _12731], clausify(left_zero)).
% 189.39/183.63
% 189.39/183.63 cnf('1',plain,[left_zero(h, phi(f_left_zero))],start(2)).
% 189.39/183.63 cnf('1.1',plain,[-(left_zero(h, phi(f_left_zero))), group_member(phi(f_left_zero), h), -(group_member(2 ^ [phi(f_left_zero), h], h))],extension(15,bind([[_12731, _12665], [phi(f_left_zero), h]]))).
% 189.39/183.63 cnf('1.1.1',plain,[-(group_member(phi(f_left_zero), h)), group_member(f_left_zero, f)],extension(9,bind([[_11356], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1',plain,[-(group_member(f_left_zero, f)), left_zero(f, f_left_zero)],extension(10,bind([[_12665, _12731], [f, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.1.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.1.1.1',plain,[-(left_zero(f, f_left_zero))],extension(12)).
% 189.39/183.63 cnf('1.1.1.1.1.1.1.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.1.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.1.1.1.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.1.1.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.1.1.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2',plain,[group_member(2 ^ [phi(f_left_zero), h], h), -(group_member(1 ^ [2 ^ [phi(f_left_zero), h]], f))],extension(4,bind([[_12254], [2 ^ [phi(f_left_zero), h]]]))).
% 189.39/183.63 cnf('1.1.2.1',plain,[group_member(1 ^ [2 ^ [phi(f_left_zero), h]], f), -(multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]])) = phi(multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]]))), group_member(f_left_zero, f)],extension(1,bind([[_11693, _11628], [1 ^ [2 ^ [phi(f_left_zero), h]], f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.1',plain,[multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]])) = phi(multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]])), -(multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]])) = phi(f_left_zero)), phi(multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]])) = phi(f_left_zero)],extension(3,bind([[_6629, _6685, _6740], [multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]])), phi(multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]])), phi(f_left_zero)]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1',plain,[multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]])) = phi(f_left_zero), -(multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero)), multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]]))],extension(3,bind([[_6740, _6629, _6685], [phi(f_left_zero), multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]), multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]]))]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.1',plain,[multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero), -(multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h])), phi(f_left_zero) = multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h])],extension(3,bind([[_6629, _6685, _6740], [multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]), phi(f_left_zero), multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h])]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.1.1',plain,[multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]), -(multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero)), multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero)],extension(3,bind([[_6629, _6685, _6740], [multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]), multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]), phi(f_left_zero)]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.1.1.1',plain,[multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero), -(left_zero(h, phi(f_left_zero))), group_member(phi(f_left_zero), h)],extension(16,bind([[_12731, _12665], [phi(f_left_zero), h]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.1.1.1.1',plain,[left_zero(h, phi(f_left_zero))],extension(2)).
% 189.39/183.63 cnf('1.1.2.1.1.1.1.1.1.2',plain,[-(group_member(phi(f_left_zero), h))],lemmata('1.1')).
% 189.39/183.63 cnf('1.1.2.1.1.1.1.1.2',plain,[-(multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero))],reduction('1.1.2.1.1.1')).
% 189.39/183.63 cnf('1.1.2.1.1.1.1.2',plain,[-(phi(f_left_zero) = multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h])), multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero)],extension(13,bind([[_6350, _6395], [multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]), phi(f_left_zero)]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.1.2.1',plain,[-(multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = phi(f_left_zero))],reduction('1.1.2.1.1.1')).
% 189.39/183.63 cnf('1.1.2.1.1.1.2',plain,[-(multiply(h, phi(f_left_zero), 2 ^ [phi(f_left_zero), h]) = multiply(h, phi(f_left_zero), phi(1 ^ [2 ^ [phi(f_left_zero), h]]))), h = h, phi(f_left_zero) = phi(f_left_zero), 2 ^ [phi(f_left_zero), h] = phi(1 ^ [2 ^ [phi(f_left_zero), h]])],extension(8,bind([[_8373, _8458, _8542, _8625, _8707, _8788], [h, h, phi(f_left_zero), phi(f_left_zero), 2 ^ [phi(f_left_zero), h], phi(1 ^ [2 ^ [phi(f_left_zero), h]])]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.2.1',plain,[-(h = h)],extension(11,bind([[_6197], [h]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.2.2',plain,[-(phi(f_left_zero) = phi(f_left_zero)), f_left_zero = f_left_zero],extension(6,bind([[_9388, _9437], [f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.2.2.1',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.2.3',plain,[-(2 ^ [phi(f_left_zero), h] = phi(1 ^ [2 ^ [phi(f_left_zero), h]])), phi(1 ^ [2 ^ [phi(f_left_zero), h]]) = 2 ^ [phi(f_left_zero), h]],extension(13,bind([[_6350, _6395], [phi(1 ^ [2 ^ [phi(f_left_zero), h]]), 2 ^ [phi(f_left_zero), h]]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.2.3.1',plain,[-(phi(1 ^ [2 ^ [phi(f_left_zero), h]]) = 2 ^ [phi(f_left_zero), h]), group_member(2 ^ [phi(f_left_zero), h], h)],extension(5,bind([[_12254], [2 ^ [phi(f_left_zero), h]]]))).
% 189.39/183.63 cnf('1.1.2.1.1.1.2.3.1.1',plain,[-(group_member(2 ^ [phi(f_left_zero), h], h))],reduction('1.1')).
% 189.39/183.63 cnf('1.1.2.1.1.2',plain,[-(phi(multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]])) = phi(f_left_zero)), multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]]) = f_left_zero],extension(6,bind([[_9388, _9437], [multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]]), f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.1.2.1',plain,[-(multiply(f, f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]]) = f_left_zero), left_zero(f, f_left_zero), group_member(1 ^ [2 ^ [phi(f_left_zero), h]], f)],extension(14,bind([[_12731, _12914, _12665], [f_left_zero, 1 ^ [2 ^ [phi(f_left_zero), h]], f]]))).
% 189.39/183.63 cnf('1.1.2.1.1.2.1.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.1.2.1.1.1',plain,[-(left_zero(f, f_left_zero))],extension(12)).
% 189.39/183.63 cnf('1.1.2.1.1.2.1.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.2.1.1.2.1.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.1.2.1.2',plain,[-(group_member(1 ^ [2 ^ [phi(f_left_zero), h]], f))],reduction('1.1.2')).
% 189.39/183.63 cnf('1.1.2.1.2',plain,[-(group_member(f_left_zero, f)), left_zero(f, f_left_zero)],extension(10,bind([[_12665, _12731], [f, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.1.1',plain,[-(left_zero(f, f_left_zero)), left_zero(f, f_left_zero), f = f, f_left_zero = f_left_zero],extension(7,bind([[_7719, _7786, _7852, _7917], [f, f, f_left_zero, f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.1.1.1',plain,[-(left_zero(f, f_left_zero))],extension(12)).
% 189.39/183.63 cnf('1.1.2.1.2.1.1.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.1.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.2',plain,[-(f = f)],extension(11,bind([[_6197], [f]]))).
% 189.39/183.63 cnf('1.1.2.1.2.1.3',plain,[-(f_left_zero = f_left_zero)],extension(11,bind([[_6197], [f_left_zero]]))).
% 189.39/183.63 %-----------------------------------------------------
% 189.39/183.64
% 189.39/183.64 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------